# Quiz 8: Interval Estimation

Statistics

Q 1Q 1

The absolute value of the difference between the point estimate and the population parameter it estimates is
A) the standard error
B) the sampling error
C) precision
D) the error of confidence

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Multiple Choice

B

Q 2Q 2

When s is used to estimate σ, the margin of error is computed by using
A) normal distribution
B) t distribution
C) the mean of the sample
D) the mean of the population

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Multiple Choice

B

Q 3Q 3

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is
A) 15
B) 2
C) 3.92
D) 4

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Multiple Choice

C

Q 4Q 4

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is
A) 5
B) 9.8
C) 650
D) 609.8

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Multiple Choice

Q 5Q 5

In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is
A) 22
B) 23
C) 60
D) 61

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Multiple Choice

Q 6Q 6

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is
A) 0.485
B) 1.96
C) 0.95
D) 1.645

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Multiple Choice

Q 7Q 7

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
A) becomes larger
B) becomes smaller
C) stays the same
D) None of these alternatives is correct.

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Multiple Choice

Q 8Q 8

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is
A) the normal distribution
B) the t distribution with n degrees of freedom
C) the t distribution with n + 1 degrees of freedom
D) the t distribution with n + 2 degrees of freedom

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Multiple Choice

Q 9Q 9

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
A) confidence level
B) interval estimate
C) parameter value
D) population estimate

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Multiple Choice

Q 10Q 10

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
A) confidence level
B) margin of error
C) parameter estimate
D) interval estimate

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Multiple Choice

Q 11Q 11

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be
A) 0.1
B) 0.95
C) 0.9
D) 0.05

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Multiple Choice

Q 12Q 12

Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?
A) standard distribution
B) z distribution
C) alpha distribution
D) t distribution

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Multiple Choice

Q 13Q 13

In interval estimation, the t distribution is applicable only when
A) the population has a mean of less than 30
B) the sample standard deviation is used to estimate the population standard deviation
C) the variance of the population is known
D) the standard deviation of the population is known

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Multiple Choice

Q 14Q 14

In developing an interval estimate, if the population standard deviation is unknown
A) it is impossible to develop an interval estimate
B) the standard deviation is arrived at using the range
C) the sample standard deviation can be used
D) it is assumed that the population standard deviation is 1

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Multiple Choice

Q 15Q 15

In order to use the normal distribution for interval estimation of μ when σ is known and the sample is very small, the population
A) must be very large
B) must have a normal distribution
C) can have any distribution
D) must have a mean of at least 1

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Multiple Choice

Q 16Q 16

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population μ).
A) The normal distribution can be used.
B) The t distribution with 5 degrees of freedom must be used.
C) The t distribution with 6 degrees of freedom must be used.
D) The sample size must be increased.

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Multiple Choice

Q 17Q 17

A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the
A) normal distribution
B) t distribution with 200 degrees of freedom
C) t distribution with 201 degrees of freedom
D) t distribution with 202 degrees of freedom

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Multiple Choice

Q 18Q 18

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the
A) normal distribution
B) t distribution with 25 degrees of freedom
C) t distribution with 26 degrees of freedom
D) t distribution with 24 degrees of freedom

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Multiple Choice

Free

Multiple Choice

Q 20Q 20

The t value for a 95% confidence interval estimation with 24 degrees of freedom is
A) 1.711
B) 2.064
C) 2.492
D) 2.069

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Multiple Choice

Q 21Q 21

As the sample size increases, the margin of error
A) increases
B) decreases
C) stays the same
D) increases or decreases depending on the size of the mean

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Multiple Choice

Q 22Q 22

For which of the following values of P is the value of P1 - P) maximized?
A) P = 0.99
B) P = 0.90
C) P = 0.01
D) P = 0.50

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Multiple Choice

Q 23Q 23

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for μ
A) becomes narrower
B) becomes wider
C) does not change
D) becomes 0.1

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Multiple Choice

Q 24Q 24

Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion
A) becomes narrower
B) becomes wider
C) does not change
D) remains the same

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Multiple Choice

Q 25Q 25

The ability of an interval estimate to contain the value of the population parameter is described by the
A) confidence level
B) degrees of freedom
C) precise value of the population mean μ
D) degrees of freedom minus 1

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Multiple Choice

Q 26Q 26

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
A) Increase the level of confidence for the interval.
B) Decrease the sample size.
C) Increase the sample size.
D) Reduce the population variance.

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Multiple Choice

Q 27Q 27

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect
A) the size of the confidence interval to increase
B) the size of the confidence interval to decrease
C) the size of the confidence interval to remain the same
D) the sample size to increase

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Multiple Choice

Q 28Q 28

In general, higher confidence levels provide
A) wider confidence intervals
B) narrower confidence intervals
C) a smaller standard error
D) unbiased estimates

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Multiple Choice

Q 29Q 29

An interval estimate is a range of values used to estimate
A) the shape of the population's distribution
B) the sampling distribution
C) a sample statistic
D) a population parameter

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Multiple Choice

Q 30Q 30

In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?
A) the maximum margin of error that can be tolerated
B) the confidence level required
C) a preliminary estimate of the true population proportion P
D) the mean of the population

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Multiple Choice

Q 31Q 31

Whenever using the t distribution for interval estimation when the sample size is very small), we must assume that
A) the sample has a mean of at least 30
B) the sampling distribution is not normal
C) the population is approximately normal
D) the finite population correction factor is necessary

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Multiple Choice

Q 32Q 32

A sample of 20 items from a population with an unknown σ is selected in order to develop an interval estimate of μ. Which of the following is not necessary?
A) We must assume the population has a normal distribution.
B) We must use a t distribution.
C) Sample standard deviation must be used to estimate σ.
D) The sample must have a normal distribution.

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Multiple Choice

Q 33Q 33

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is
A) 105.0 to 225.0
B) 175.0 to 185.0
C) 100.0 to 200.0
D) 170.2 to 189.8

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Multiple Choice

Q 34Q 34

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of
A) 7.84
B) 31.36
C) 344.96
D) 1,936

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Multiple Choice

Q 35Q 35

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is
A) 15.2 to 24.8
B) 19.200 to 20.800
C) 19.216 to 20.784
D) 21.2 to 22.8

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Multiple Choice

Q 36Q 36

When the level of confidence decreases, the margin of error
A) stays the same
B) becomes smaller
C) becomes larger
D) becomes smaller or larger, depending on the sample size

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Multiple Choice

Q 37Q 37

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is
A) 20.5 to 26.5
B) 24.4 to 25.6
C) 23.0 to 27.0
D) 20.0 to 30.0

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Multiple Choice

Q 38Q 38

A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is
A) 76.00 to 84.00
B) 77.40 to 86.60
C) 83.00 to 85.00
D) 68.00 to 100.00

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Multiple Choice

Q 39Q 39

The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is
A) 10
B) 11
C) 116
D) 117

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Multiple Choice

Q 40Q 40

It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
A) 25
B) 74
C) 189
D) 75

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Multiple Choice

Q 41Q 41

When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals
A) n-1
B) n
C) 29
D) 30

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Multiple Choice

Q 42Q 42

The following random sample from a population whose values were normally distributed was collected. 10 8 11 11 The 95% confidence interval for μ is
A) 8.52 to 10.98
B) 7.75 to 12.25
C) 9.75 to 10.75
D) 8.00 to 10.00

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Multiple Choice

Q 43Q 43

The following random sample from a population whose values were normally distributed was collected. 10 12 18 16 The 80% confidence interval for μ is
A) 12.054 to 15.946
B) 10.108 to 17.892
C) 10.321 to 17.679
D) 11.009 to 16.991

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Multiple Choice

Q 44Q 44

Which of the following best describes the form of the sampling distribution of the sample proportion?
A) When standardized, it is exactly the standard normal distribution.
B) When standardized, it is the t distribution.
C) It is approximately normal as long as n ≥ 30.
D) It is approximately normal as long as np ≥ 5 and n1p) ≥ 5.

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Multiple Choice

Q 45Q 45

In a random sample of 144 observations, = 0.6. The 95% confidence interval for P is
A) 0.52 to 0.68
B) 0.144 to 0.200
C) 0.60 to 0.70
D) 0.50 to 0.70

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Multiple Choice

Q 46Q 46

In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is
A) 0.122 to 0.278
B) 0.164 to 0.236
C) 0.134 to 0.266
D) 0.120 to 0.280

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Multiple Choice

Q 47Q 47

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is
A) 0.419 to 0.481
B) 0.40 to 0.50
C) 0.45 to 0.55
D) 1.645 to 1.96

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Multiple Choice

Q 48Q 48

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is
A) 110
B) 111
C) 216
D) 217

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Multiple Choice

Q 49Q 49

We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?
A) 200
B) 100
C) 58
D) 385

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Multiple Choice

Q 50Q 50

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
A) 0.871 to 0.929
B) 0.120 to 0.280
C) 0.765 to 0.835
D) 0.071 to 0.129

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Multiple Choice

Q 51Q 51

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
A) becomes larger
B) becomes smaller
C) stays the same
D) becomes negative

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Multiple Choice

Q 52Q 52

In order to estimate the average time spent on the computer terminals per student, data were collected for a sample of 49 business students over a one week period. Assume the population standard deviation is 1.4 hours. The standard error of the mean is
A) 0.20
B) 0.30
C) 5
D) 7

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Multiple Choice

Q 53Q 53

Exhibit 8-1
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is
1.8 hours.
-Refer to Exhibit 8-1. The standard error of the mean is
A) 7.50
B) 0.39
C) 2.00
D) 0.20

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Multiple Choice

Q 54Q 54

Exhibit 8-1
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is
1.8 hours.
-Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately
A) 0.39
B) 1.96
C) 0.20
D) 1.64

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Multiple Choice

Q 55Q 55

Exhibit 8-1
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is
1.8 hours.
-Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is
A) 7.04 to 110.96 hours
B) 7.36 to 10.64 hours
C) 7.80 to 10.20 hours
D) 8.61 to 9.39 hours

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Multiple Choice

Q 56Q 56

Exhibit 8-2
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.
-Refer to Exhibit 8-2. If we are interested in determining an interval estimate for μ at 96.6% confidence, the Z value to use is
A) 1.96
B) 0.483
C) 2.12
D) 1.645

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Multiple Choice

Q 57Q 57

Exhibit 8-2
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.
-Refer to Exhibit 8-2. The standard error of the mean is
A) 22.00
B) 96.60
C) 4.24
D) 2.00

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Multiple Choice

Q 58Q 58

Exhibit 8-2
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.
-Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.9, the standard error of the mean
A) will increase
B) will decrease
C) remains unchanged
D) becomes negative

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Multiple Choice

Q 59Q 59

Exhibit 8-2
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.
-Refer to Exhibit 8-2. The 96.6% confidence interval for μ is
A) 63.00 to 67.00
B) 60.76 to 69.24
C) 61.08 to 68.92
D) 60.00 to 80.00

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Multiple Choice

Q 60Q 60

Exhibit 8-2
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.
-Refer to Exhibit 8-2. If the sample size was 100 other factors remain unchanged), the interval for μ would
A) not change
B) become narrower
C) become wider
D) become zero

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Multiple Choice

Q 61Q 61

Exhibit 8-3
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute.
-Refer to Exhibit 8-3. The standard error of the mean equals
A) 0.001
B) 0.010
C) 0.100
D) 1.000

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Multiple Choice

Q 62Q 62

Exhibit 8-3
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute.
-Refer to Exhibit 8-3. With a .95 probability, the sample mean will provide a margin of error of
A) 1.96
B) 0.10
C) 0.196
D) 1.64

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Multiple Choice

Q 63Q 63

Exhibit 8-3
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute.
-Refer to Exhibit 8-3. The 95% confidence interval for the true average checkout time in minutes) is
A) 3:00 to 5:00
B) 1.36 to 4.64
C) 1.00 to 5.00
D) 2.804 to 3.196

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Multiple Choice

Q 64Q 64

Exhibit 8-4
In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours.
-Refer to Exhibit 8-4. The standard error of the mean is
A) 450
B) 81
C) 500
D) 50

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Multiple Choice

Q 65Q 65

Exhibit 8-4
In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours.
-Refer to Exhibit 8-4. At 95% confidence, the size of the margin of error is
A) 1.96
B) 50
C) 98
D) 42

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Multiple Choice

Q 66Q 66

Exhibit 8-4
In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours.
-Refer to Exhibit 8-4. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is
A) 1,760 to 1,956 KWH
B) 1,858 to 1,956 KWH
C) 1,760 to 1,858 KWH
D) none of these alternatives is correct

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Multiple Choice

Q 67Q 67

Exhibit 8-5
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.
-Refer to Exhibit 8-5. If we want to provide a 95% confidence interval for the SAT scores, the degrees of freedom for reading the critical values of "t" statistic is
A) 60
B) 61
C) 62
D) 63

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Multiple Choice

Q 68Q 68

Exhibit 8-5
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.
-Refer to Exhibit 8-5. The "t" value for this interval estimation is
A) 1.96
B) 1.998
C) 1.64
D) 1.28

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Multiple Choice

Q 69Q 69

Exhibit 8-5
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.
-Refer to Exhibit 8-5. The margin of error at 95% confidence is
A) 1.998
B) 1400
C) 240
D) 59.95

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Multiple Choice

Q 70Q 70

Exhibit 8-5
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.
-Refer to Exhibit 8-5. The 95% confidence interval for the SAT scores is
A) 1340.05 to 1459.95
B) 1400 to 1459.95
C) 1340.05 to 1400
D) 1400 to 1600

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Multiple Choice

Q 71Q 71

Exhibit 8-6
A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of
$7.00.
-Refer to Exhibit 8-6. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is
A) 1.96
B) 1.64
C) 1.28
D) 1.993

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Multiple Choice

Q 72Q 72

Exhibit 8-6
A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of
$7.00.
-Refer to Exhibit 8-6. The standard error of the mean is
A) 80.83
B) 7
C) 0.8083
D) 1.611

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Multiple Choice

Q 73Q 73

Exhibit 8-6
A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of
$7.00.
-Refer to Exhibit 8-6. The value of the margin of error at 95% confidence is
A) 80.83
B) 7
C) 0.8083
D) 1.611

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Multiple Choice

Q 74Q 74

Exhibit 8-6
A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of
$7.00.
-Refer to Exhibit 8-6. The 95% confidence interval for the average hourly wage of all information system managers is
A) 40.75 to 42.36
B) 39.14 to 40.75
C) 39.14 to 42.36
D) 30 to 50

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Multiple Choice

Q 75Q 75

A random sample of 87 airline pilots had an average yearly income of $99,400 with a standard deviation of $12,000.
a. If we want to determine a 95% confidence interval for the average yearly income, what is the value of t?
b. Develop a 95% confidence interval for the average yearly income of all pilots.

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Essay

Q 76Q 76

A random sample of 81 credit sales in a department store showed an average sale of $68.00. From past data, it is known that the standard deviation of the population is $27.00.
a. Determine the standard error of the mean.
b. With a 0.95 probability, what can be said about the size of the margin of error?
c. What is the 95% confidence interval of the population mean?

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Essay

Q 77Q 77

You are given the following information obtained from a sample of 5 observations taken from a population that has a normal distribution.
94 72 93 54 77
Develop a 98% confidence interval estimate for the mean of the population.

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Short Answer

Q 78Q 78

Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective.
a. Determine a 95% confidence interval for the percentage of defective systems.
b. If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales.

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Essay

Q 79Q 79

Choo Choo Paper Company produces papers of various thickness. A random sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. Develop a 95% confidence interval for the mean thickness of the population.

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Short Answer

Q 80Q 80

The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of
$24.
a. Construct a 90% confidence interval for the mean monthly electric bills of all residents.
b. Construct a 95% confidence interval for the mean monthly electric bills of all residents.

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Essay

Q 81Q 81

In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

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Short Answer

Q 82Q 82

Two hundred students are enrolled in an Economics class. After the first examination, a random sample of 6 papers was selected. The grades were 65, 75, 89, 71, 70 and 80.
a. Determine the standard error of the mean.
b. What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why.
c. Assume the assumption of Part b is met. Provide a 95% confidence interval for the mean grade of all the students in the class.

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Essay

Q 83Q 83

A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. He reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. He neglected to report what confidence coefficient he had used. Based on the above information, determine the confidence coefficient that was used. Assume the population has a normal distribution.

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Short Answer

Q 84Q 84

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?

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Short Answer

Q 85Q 85

A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces.
a. Construct a 68.26% confidence interval for the mean of the population.
b. Construct a 97% confidence interval for the mean of the population.
c. Discuss why the answers in Parts a and b are different.

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Essay

Q 86Q 86

You are given the following information obtained from a random sample of 5 observations taken from a large population.
32 34 32 30 32
Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

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Short Answer

Q 87Q 87

In a sample of 200 individuals, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of people in the population who are Democrats.

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Short Answer

Q 88Q 88

A random sample of 121 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $44. Develop a 95% confidence interval estimate for the mean of the population.

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Short Answer

Q 89Q 89

A sample of 60 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population.

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Short Answer

Q 90Q 90

A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The standard deviation of the population is known to be $66.
a. Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain.
b. Find the standard error of the mean.
c. Give a point estimate of the population mean.
d. Construct a 80% confidence interval estimates for the mean.
e. Construct a 95% confidence interval for the mean.

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Essay

Q 91Q 91

A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 45 minutes with a standard deviation of 14 minutes.
a. Compute the standard error of the mean.
b. With a .95 probability, what statement can be made about the size of the margin of error?
c. Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant.
d. With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?

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Essay

Q 92Q 92

A random sample of 81 students at a local university showed that they work an average of 60 hours per month with a standard deviation of 18 hours. Compute a 95% confidence interval for the mean of the population.

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Short Answer

Q 93Q 93

It is known that the variance of a population equals 1296. A random sample of 144 observations is going to be taken from the population.
a. With a 0.95 probability, what statement can be made about the size of the margin of error?
b. With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 6 or less?

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Essay

Q 94Q 94

The makers of a soft drink want to identify the average age of its consumers. A sample of 55 consumers was taken. The average age in the sample was 21 years with a standard deviation of 4 years.
a. Construct a 95% confidence interval for the true average age of the consumers.
b. Construct an 80% confidence interval for the true average age of the consumers.
c. Discuss why the 95% and 80% confidence intervals are different.

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Q 95Q 95

A random sample of 53 observations was taken. The average in the sample was 90 with a variance of 400.
a. Construct a 98% confidence interval for μ.
b. Construct a 99% confidence interval for μ.
c. Discuss why the 98% and 99% confidence intervals are different.
d. What would you expect to happen to the confidence interval in Part a if the sample size was increased? Be sure to explain your answer.

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Q 96Q 96

You are given the following information obtained from a random sample of 6 observations. Assume the population has a normal distribution.
14 20 21 16 18 19
a. What is the point estimate of μ?
b. Construct an 80% confidence interval for μ.
c. Construct a 98% confidence interval for μ.
d. Discuss why the 80% and 98% confidence intervals are different.

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Q 97Q 97

Below you are given ages that were obtained by taking a random sample of 9 undergraduate students. Assume the population has a normal distribution.
40 42 43 39 37 39
a. What is the point estimate of μ?
b. Determine the standard deviation.
c. Construct a 90% confidence interval for the average age of undergraduate students.
d. Construct a 99% confidence interval for the average age of undergraduate students.
e. Discuss why the 99% and 90% confidence intervals are different.

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Q 98Q 98

A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school.
a. Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school.
b. Using the results of the pilot study with a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

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Q 99Q 99

A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below.
a. What is the point estimate for the proportion of people who liked the chocolate bar?
b. Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar.
c. With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 3% or less?

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Q 100Q 100

If the population standard deviation of the lifetime of washing machines is estimated to be 900 hours, how large a sample must be taken in order to be 97% confident that the margin of error will not exceed 100 hours?

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Q 101Q 101

The manager of a department store wants to determine what proportion of people who enter the store use the store's credit cards for their purchases. What size sample should he take so that at 95% confidence the error will not be more than 6%?

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Q 102Q 102

In order to estimate the average electric usage per month, a sample of 196 houses was selected, and their electric usage determined.
a. Assume a population standard deviation of 350-kilowatt hours. Determine the standard error of the mean.
b. With a 0.95 probability, determine the margin of error.
c. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?

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Q 103Q 103

A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00.
a. Determine the standard error of the mean.
b. With a 0.95 probability, determine the margin of error.
c. What is the 95% confidence interval of the population mean?

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Q 104Q 104

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 16 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds.
a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

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Q 105Q 105

A small stock brokerage firm wants to determine the average daily sales in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000.
a. Provide a 95% confidence interval estimate for the average daily sale.
b. Provide a 97% confidence interval estimate for the average daily sale.

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Q 106Q 106

A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.8 days. Provide a 95% confidence interval for the average number of days absent per term for all the children.

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Q 107Q 107

The Highway Safety Department wants to study the driving habits of individuals. A sample of 121 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.

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Q 108Q 108

In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours with a standard deviation of 3.2 hours watching TV per week.
a. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.
Assume that a sample of 62 students was selected with the same mean and the standard
b. deviation). Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.

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Q 109Q 109

Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 64 transactions yielded a mean of 6 seconds with a standard deviation of 0.8 seconds. Determine a 98% confidence interval for the average CPU time.

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Q 110Q 110

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 53 customers revealed an average age of 28 years with a standard deviation of 4 years. Determine a 98% confidence interval estimate for the average age of all his customers.

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Q 111Q 111

A sample of 36 patients in a doctor's office showed that they had to wait an average of 45 minutes with a standard deviation of 10 minutes before they could see the doctor. Provide a 90% confidence interval estimate for the average waiting time of all the patients who visit this doctor.

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Q 112Q 112

The monthly starting salaries of students who receive an MBA degree have a population standard deviation of
$110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less?

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Q 113Q 113

A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily output is 200 tons, how many days should they sample so that the margin of error will be 39.2 tons or less?

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Short Answer

Q 114Q 114

If the standard deviation of the lifetime of a vacuum cleaner is estimated to be 300 hours, how large of a sample must be taken in order to be 97% confident that the margin of error will not exceed 40 hours?

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Q 115Q 115

A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital.
a. Provide a 95% confidence interval for all the patients who are referred to the health center by the hospital.
b. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of 0.04 or less at 95% confidence?

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Q 116Q 116

In a random sample of 400 residents of Chattanooga, 320 residents indicated that they voted for the Democratic candidate in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Chattanooga residents who voted for the Democratic candidate.

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Q 117Q 117

The manager of a grocery store wants to determine what proportion of people who enter his store are his regular customers. What size sample should he take so that at 97% confidence the margin of error will not be more than 0.1?

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Q 118Q 118

The average score of a sample of 87 senior business majors at UTC who took the Graduate Management Admission Test was 510 with a standard deviation of 36. Provide a 98% confidence interval for the mean of the population.

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Q 119Q 119

In a poll of 600 voters in a campaign to eliminate non-returnable beverage containers, 210 of the voters were opposed. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill.

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Q 120Q 120

A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.7 to 12.3 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.28, determine the size of the sample.

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Q 121Q 121

A simple random sample of 144 items resulted in a sample mean of 1257.85 and a standard deviation of 480. Develop a 95% confidence interval for the population mean.

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Q 122Q 122

A simple random sample of 36 items resulted in a sample mean of 40 and a standard deviation of 12. Construct a 95% confidence interval for the population mean.

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Q 123Q 123

An Excel printout of the descriptive measures of daily checking account balances in dollars) of customers of First Daisy Bank is shown below. Develop a 95% confidence interval estimate for the mean of the population of the checking balances.
Account Balance Information

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Q 124Q 124

Information regarding the price of a roll of camera film 35 mm, 24 exposure) for a sample of 12 cities worldwide is shown below. Determine a 95% confidence interval for the population mean.
Price of Film Information

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Q 125Q 125

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds.
a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

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Q 126Q 126

A local electronics firm wants to determine their average daily sales in dollars.) A sample of the sales for 36 days revealed average sales of $139,000. Assume that the standard deviation of the population is known to be
$12,000.
a. Provide a 95% confidence interval estimate for the average daily sales.
b. Provide a 97% confidence interval estimate for the average daily sales.

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Q 127Q 127

The Highway Safety Department wants to study the driving habits of individuals. A sample of 81 cars traveling on the highway revealed an average speed of 67 miles per hour with a standard deviation of 9 miles per hour.
a. Compute the standard error of the mean.
b. Determine a 99% confidence interval estimate for the speed of all cars.

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Q 128Q 128

In order to determine the summer unemployment rate among college students, a pilot sample was taken; and it was determined that ten percent of the individuals in the sample were unemployed. Using the results of the pilot study and a 95% confidence, what size sample would be required to estimate the proportion of unemployed college students if we want the margin of error not to exceed 3 percent?

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