# Quiz 9: Estimation and Confidence Intervals

Statistics

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Q 4Q 4

An interval estimate is a range of values in which the population parameter is likely to occur.

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Q 5Q 5

A sample of 2,000 union members was selected,and a survey recorded their opinions regarding a proposed management union contract. A total of 1,600 members were in favor of it. A 95% confidence interval estimated that the population proportion was between 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

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Q 6Q 6

A confidence interval for a population proportion uses the uniform distribution to approximate the binomial distribution.

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Q 7Q 7

The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

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Q 8Q 8

One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99,but it may be any degree of confidence you specify.

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Q 9Q 9

The population variation has little or no effect in determining the size of a sample selected from the population.

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Q 10Q 10

To determine the value of the standard error of the mean,the standard deviation is divided by the sample size.

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Q 11Q 11

To determine the size of a sample,the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

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Q 12Q 12

When using the t-distribution to calculate a confidence interval,we assume that the population of interest is normal or nearly normal.

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Q 13Q 13

A z-statistic is used for a problem involving any sample size and an unknown population standard deviation.

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Q 14Q 14

The finite population correction (FPC)factor is used to adjust the z-statistic or t-statistic.

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Q 16Q 16

The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.90 degree of confidence. For a small pilot study,the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days,how many salespeople should be sampled?
A)133
B)452
C)511
D)2,100

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Multiple Choice

Q 17Q 17

A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 0.95 degree of confidence is to be used. Several years ago,a study revealed that 21% of junior executives left their company within three years. To update this study,how many junior executives should be surveyed?
A)594
B)612
C)709
D)897

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Multiple Choice

Q 18Q 18

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed,350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient,what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?
A)0.647 and 0.753
B)0.612 and 0.712
C)0.397 and 0.797
D)0.826 and 0.926

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Multiple Choice

Q 19Q 19

A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence,what is the confidence interval for the population mean?
A)6.99 and 7.99
B)4.15 and 7.15
C)6.14 and 6.86
D)6.49 and 7.49

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Multiple Choice

Q 20Q 20

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?
A)14.7 and 16.9
B)13.2 and 17.6
C)10.0 and 20.0
D)16.1 and 18.1

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Multiple Choice

Q 21Q 21

A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an interval of $75 is desired,how many customers should be sampled?
A)44
B)212
C)629
D)87

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Multiple Choice

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Q 23Q 23

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles,with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?
A)50,000
B)3,500
C)500
D)35

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Multiple Choice

Q 24Q 24

What is the interpretation of a 96% confidence level?
A)There's a 96% chance that the given interval includes the true value of the population parameter.
B)Approximately 96 out of 100 such intervals would include the true value of the population parameter.
C)There's a 4% chance that the given interval does not include the true value of the population parameter.
D)The interval contains 96% of all sample means.

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Multiple Choice

Q 25Q 25

Which statement(s)is(are)correct about the t-distribution?
A)The mean is zero.
B)Its shape is symmetric.
C)Its dispersion is based on degrees of freedom.
D)All apply.

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Q 26Q 26

What kind of distribution is the t-distribution?
A)Continuous
B)Discrete
C)Subjective
D)A z-distribution

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Q 27Q 27

How is the t-distribution similar to the standard z-distribution?
A)Both are discrete distributions.
B)Both are skewed distributions.
C)Both are families of distributions.
D)Both are continuous distributions.

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Multiple Choice

Q 28Q 28

A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean,what number of degrees of freedom should be used to determine the appropriate t-value?
A)20
B)19
C)21
D)25

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Multiple Choice

Q 29Q 29

Of the following characteristics,the t-distribution and z-distribution are the same in all but one. Which one is it?
A)Continuous
B)Symmetrical
C)Bell-shaped
D)Mean = 0,and standard deviation = 1

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Multiple Choice

Q 30Q 30

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence,what is the interval estimate for the population proportion (to the nearest 10th of a percent)?
A)78.2% to 81.8%
B)69.2% to 86.4%
C)76.5% to 83.5%
D)77.7% to 82.3%

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Multiple Choice

Q 31Q 31

Which of the following is not necessary to determine how large a sample to select from a population?
A)The level of confidence in estimating the population parameter
B)The size of the population
C)The maximum allowable error in estimating the population parameter
D)An estimate of the population variation

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Multiple Choice

Q 32Q 32

A sample mean is the best point estimate of ________.
A)the population standard deviation
B)the population median
C)the population mean
D)the sample standard deviation

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Q 33Q 33

A sample standard deviation is the best point estimate of the ________.
A)population range
B)population skewness
C)population mode
D)population standard deviation

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Multiple Choice

Q 34Q 34

A confidence interval for a population mean ________.
A)estimates the population range
B)estimates a likely interval for a population mean
C)estimates likelihood or probability
D)estimates the population standard deviation

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Multiple Choice

Q 35Q 35

Knowing the population standard deviation,a 95% confidence interval infers that the population mean ________.
A)is between 0 and 100%
B)is within ±1.96 standard deviations of the sample mean
C)is within ±1.96 standard errors of the sample mean
D)is too large

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Multiple Choice

Q 36Q 36

When a confidence interval for a population mean is constructed from sample data,________.
A)we can conclude that the population mean is in the interval
B)we can conclude that the population mean is not in the interval
C)we can conclude,for an infinite number of samples and corresponding confidence intervals,that the population mean is in a stated percentage of the intervals
D)we cannot make any inferences

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Multiple Choice

Q 37Q 37

The distribution of Student's t has ________.
A)a mean of zero and a standard deviation of one
B)a mean of one and a standard deviation of one
C)a mean of zero and a standard deviation that depends on the sample size
D)a mean that depends on the sample size and a standard deviation of one

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Multiple Choice

Q 38Q 38

The distribution of Student's t is ________.
A)symmetrical
B)negatively skewed
C)positively skewed
D)a discrete probability distribution

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Multiple Choice

Q 39Q 39

When using Student's t to compute an interval estimate,________.
A)we assume that the samples are collected from populations that are uniformly distributed
B)we estimate the population mean based on the sample mean
C)we use the z-distribution
D)we assume that the samples are collected from normally distributed populations

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Multiple Choice

Q 40Q 40

A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence,what is the confidence interval for the population mean?
A)5.04 and 5.96
B)5.06 and 5.94
C)2.67 and 8.33
D)4.40 and 6.60

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Multiple Choice

Q 41Q 41

When we use a confidence interval to reach a conclusion about the population mean,we are applying a type of reasoning or logic called ________.
A)descriptive statistics
B)the normal distribution
C)statistical inference
D)graphics

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Multiple Choice

Q 42Q 42

A local company wants to evaluate their quality of service by surveying their customers. Their budget limits the number of surveys to 100. What is their maximum error of the estimated mean quality for a 95% level of confidence and an estimated standard deviation of 5?
A)0.9604
B)0.98
C)1.96
D)5%

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Multiple Choice

Q 43Q 43

A local retail company wants to estimate the mean amount spent by customers. Their store's budget limits the number of surveys to 225. What is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00?
A)$10.00
B)$1.00
C)1%
D)$1.72

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Multiple Choice

Q 44Q 44

A university surveyed recent graduates of the English department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000,with a standard deviation of $2,500. What is the best point estimate of the population mean?
A)$25,000
B)$2,500
C)$400
D)$62.5

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Multiple Choice

Q 45Q 45

A university surveyed recent graduates of the English department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation was $2,500. What is the 95% confidence interval for the mean salary of all graduates from the English department?
A)[$22,500,$27,500]
B)[$24,755,$25,245]
C)[$24,988,$25,012]
D)[$24,600,$25,600]

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Multiple Choice

Q 46Q 46

A university surveyed recent graduates of the English department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation is $2,500. A 95% confidence interval is constructed. What does the confidence interval mean?
A)The population mean is in the interval.
B)The population mean is not in the interval.
C)The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95.
D)There is a 5% chance that the computed interval does not contain the population mean.

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Multiple Choice

Q 47Q 47

A survey of an urban university (population of 25,450)showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence,what is the confidence interval for the proportion of students supporting the fee increase?
A)[0.767,0.815]
B)[0.759,0.822]
C)[0.771,0.811]
D)[0.714,0.866]

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Multiple Choice

Q 48Q 48

A survey of an urban university (population of 25,450)showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 99% level of confidence,what is the confidence interval for the proportion of students supporting the fee increase?
A)[0.751,0.829]
B)[0.759,0.823]
C)[0.767,0.814]
D)[0.771,0.811]

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Multiple Choice

Q 49Q 49

University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75,0.85],what conclusion can be drawn?
A)Seventy percent is not in the interval,so another sample is needed.
B)Seventy percent is not in the interval,so assume it will not be supported.
C)The interval estimate is above 70%,so infer that it will be supported.
D)Since this was not based on the population,no conclusion can be drawn.

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Multiple Choice

Q 50Q 50

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week. Assuming a population standard deviation of six hours,what is the required sample size if the error should be less than a half hour with a 95% level of confidence?
A)554
B)130
C)35
D)393

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Multiple Choice

Q 51Q 51

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week. Assuming a population standard deviation of three hours,what is the required sample size if the error should be less than a half hour with a 99% level of confidence?
A)196
B)239
C)15
D)16

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Multiple Choice

Q 52Q 52

A group of statistics students decided to conduct a survey at their university to estimate the average (mean)amount of time students spent studying per week. They sampled 554 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours,what is the 95% level of confidence?
A)[21.80,22.80]
B)[16.3,28.3]
C)[21.64,22.96]
D)[20.22,22.0]

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Multiple Choice

Q 53Q 53

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours,what is the 99% level of confidence?
A)[21.80,22.80]
B)[16.3,28.3]
C)[21.30,23.30]
D)[20.22,22.0]

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Multiple Choice

Q 54Q 54

A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours,what is the required sample size if the error should be less than a half hour?
A)196
B)98
C)10
D)16

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Multiple Choice

Q 55Q 55

A survey of 50 retail stores revealed that the average price of a microwave was $375,with a sample standard deviation of $20. Assuming the population is normally distributed,what is the 95% confidence interval to estimate the true cost of the microwave?
A)$323.40 to $426.60
B)$328.40 to $421.60
C)$350.80 to $395.80
D)$369.31 to $380.69

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Multiple Choice

Q 56Q 56

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a sample standard deviation of $20. Assuming the population is normally distributed,what is the 99% confidence interval to estimate the true cost of the microwave?
A)$367.42 to $382.58
B)$315.00 to $415.00
C)$323.40 to $426.60
D)$335.82 to $414.28

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Multiple Choice

Q 57Q 57

A survey of 50 retail stores revealed that the average price of a microwave was $375,with a sample standard deviation of $20. If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave,what similarities would they have?
A)Both have the same confidence level.
B)Both use the same t-statistic.
C)Both use the same z-statistic.
D)Both use the same point estimate of the population mean.

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Multiple Choice

Q 58Q 58

If 95% and 98% confidence intervals were developed to estimate the true cost of an MP3 player with a known population standard deviation,what differences would they have?
A)The standard errors would be different.
B)The point estimates of the population mean would be different.
C)The sample sizes would be different.
D)The z-statistics would be different.

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Multiple Choice

Q 59Q 59

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the best point estimate for the population mean?
A)2.1 years
B)1.5 years
C)19.1 years
D)9 years

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Multiple Choice

Q 60Q 60

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years,with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?
A)[0.97,3.27]
B)[15.64,22.56]
C)[17.97,20.23]
D)[17.95,20.25]

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Multiple Choice

Q 61Q 61

A student wanted to construct a 99% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean?
A)[17.42,20.78]
B)[17.48,20.72]
C)[14.23,23.98]
D)[0.44,3.80]

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Multiple Choice

Q 62Q 62

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98,with a standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a gallon of milk?
A)$2.81 to $3.15
B)$2.94 to $3.02
C)$2.77 to $3.19
D)$2.95 to $3.01

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Multiple Choice

Q 63Q 63

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98,with a standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?
A)$2.73 to $3.23
B)$2.85 to $3.11
C)$2.94 to $3.02
D)$2.95 to $3.01

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Multiple Choice

Q 64Q 64

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98,with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk,what similarities would they have?
A)Both have the same confidence level.
B)Both use the same t-statistic.
C)Both use the same z-statistic.
D)Both use the same point estimate of the population mean.

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Multiple Choice

Q 65Q 65

A survey of an urban university (population of 25,450)showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 99% level of confidence,what is the confidence interval for the proportion of students attending a football game?
A)[0.7671,0.8143]
B)[0.6550,0.7050]
C)[0.6464,0.7172]
D)[0.6805,0.6815]

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Multiple Choice

Q 66Q 66

A survey of an urban university (population of 25,450)showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence,what is the confidence interval for the proportion of students attending a football game?
A)[0.7510,0.8290]
B)[0.6592,0.7044]
C)[0.6659,0.6941]
D)[0.6795,0.6805]

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Multiple Choice

Q 67Q 67

A survey of households in a small town showed that in 850 of 1,200 sampled households,at least one member attended a town meeting during the year. Using the 99% level of confidence,what is the confidence interval for the proportion of households represented at a town meeting?
A)[0.674,0.742]
B)[0.655,0.705]
C)[0.665,0.694]
D)[0.679,0.680]

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Multiple Choice

Q 68Q 68

A survey of households in a small town showed that in 500 of 1,200 sampled households,at least one member attended a town meeting during the year. Using the 95% level of confidence,what is the confidence interval for the proportion of households represented at a town meeting?
A)[0.417,0.427]
B)[0.389,0.445]
C)[0.400,0.417]
D)[0.417,0.445]

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Multiple Choice

Q 69Q 69

A sample of 25 is selected from a known population of 100 elements. What is the finite population correction factor?
A)8.66
B)75
C)0.87
D)Cannot be determined

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Multiple Choice

Q 70Q 70

A sample of 50 is selected from a known population of 250 elements. The population standard deviation is 15. Using the finite correction factor,what is the standard error of the sample means?
A)2.89
B)1.90
C)2.12
D)Cannot be determined

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Multiple Choice

Q 71Q 71

A sample of 100 students is selected from a known population of 1,000 students to construct a 95% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?
A)0.949
B)0.901
C)1.96
D)Cannot be determined

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Multiple Choice

Q 72Q 72

A sample of 100 is selected from a known population of 350 elements. The population standard deviation is 15. Using the finite correction factor,what is the standard error of the sample means?
A)12.6773
B)0.8452
C)1.2695
D)Cannot be determined

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Multiple Choice

Q 73Q 73

A sample of 500 students is selected from a known population of 15,000 students to construct a 99% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?
A)0.9499
B)0.9832
C)2.5760
D)Cannot be determined

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Multiple Choice

Q 74Q 74

A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean (x-bar)is 300. What is the margin of error at the 95% confidence level?
A)±8
B)±93
C)±7
D)±08

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Multiple Choice

Q 75Q 75

As the sample size for a t-distribution increases,the differences between the t-distribution and the standard normal distribution ________.
A)are unchanged and remain the same
B)become smaller,as the t-distribution approaches the standard normal distribution
C)become greater
D)are evident because the tails of the t-distribution become thicker

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Multiple Choice

Q 76Q 76

The z-score or z-value corresponding to a 95.34% confidence interval is ________.
A)1.96
B)1.65
C)1.99
D)1.68

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Multiple Choice

Q 77Q 77

Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________.
A)[0.541,0.639]
B)[0.400,0.600]
C)[0.500,0.700]
D)[0.565,0.635]

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Multiple Choice