Deck 10: Introduction to Estimation

Question 1

If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

Answer 1

larger
bigger
greater
more

Question 2

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

Answer 2

False

Question 3

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

A)62
B)61
C)8
D)None of these choices.

Answer 3

62

Question 4

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was

A)90%
B)95%
C)99%
D)None of these choices.

Question 5

The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

Question 6

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.

Question 7

The sample size needed to estimate the population mean was found to be 865. If the value of the population standard deviation was 75, and the maximum allowable error was 5, then the confidence level used was 95%.

Question 8

Which of the following statements is false regarding the sample size needed to estimate a population mean?

A)It is directly proportional to the population variance.
B)It is directly proportional to the square of z _{$\alpha$ / 2}.
C)It is directly proportional to the square of the maximum allowable error B.
D)None of these choices.

Question 9

If the bound on the error of estimation decreases, the sample size ____________________.

Question 10

When determining the required sample size for a confidence interval, you need to know the population ____________________, the confidence ____________________, and the ____________________ on the error of estimation.

Question 11

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

Question 12

If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

Question 13

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:

A)166
B)167
C)13
D)None of these choices.

Question 14

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

Question 15

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:

A)99%
B)95%
C)90%
D)None of these choices.

Question 16

The error of estimation is the ____________________ between an estimator and the parameter.

Question 17

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

Question 18

When determining the sample size necessary for estimating the true population mean, which factor is not of our concern when sampling with replacement?

A)The allowable or tolerable sampling error.
B)The level of confidence desired in the estimate.
C)The population standard deviation.
D)The population size.

Question 19

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

Question 20

In determining the sample size n needed to estimate the population mean, n decreases as the desired width of the confidence interval decreases.

Question 21

NARRBEGIN: College Dean
College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.NARREND
{College Dean Narrative} What sample size should be used if the standard deviation is changed to 50?

Question 22

In the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ , the subscript $\alpha$ / 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

Question 23

NARRBEGIN: College Dean
College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.NARREND
{College Dean Narrative} What sample size should be used?

Question 24

The width of a 95% confidence interval is 0.95.

Question 25

NARRBEGIN: College Dean
College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.NARREND
{College Dean Narrative} What sample size should be used if using a 95% confidence level?

Question 26

An electronics retailer is interested in studying the incomes of consumers in a particular area. The population standard deviation is known to be $1,000. What sample size would the researcher need to use for a 95% confidence interval if the difference between UCL and LCL should not be more than $100?

Question 27

The larger the confidence level used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

Question 28

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

Question 29

The bound on the error of estimation is the ____________________ amount of sampling error that we are willing to tolerate.

Question 30

The difference between the sample statistic and actual value of the population parameter is the confidence level of the estimate.

Question 31

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

Question 32

NARRBEGIN: College Dean
College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.NARREND
{College Dean Narrative} What sample size should be used if we wish to estimate the population mean to within 10 units?

Question 33

As the bound on the error of estimation decreases, the sample size ____________________.

Question 34

In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

Question 35

The term 1 - $\alpha$ refers to the probability that a confidence interval does not contain the population parameter.

Question 36

An engineer for an electric fencing company is interested in the mean length of wires being cut automatically by machine. The desired length of the wires is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. Suppose the engineer decided to estimate the mean length to within 0.025 with 99% confidence. What sample size would be needed?

Question 37

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 8. The interval estimate was 50.0 $\pm$ 2.50. Had $\sigma$ equaled 16, the interval estimate would be 100 $\pm$ 5.0.

Question 38

One can reduce the width of a confidence interval by taking a smaller sample size.

Question 39

A research firm has been contracted to estimate the mean weekly family expenditure on clothes. He believes that the standard deviation of the weekly expenditure is $125. Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

Question 40

How large a sample of federal employees in Nevada should be taken if we want to estimate with 98% confidence the mean salary to within $2,000. The population standard deviation is assumed to be $10,500.

Question 41

Which of the following is an incorrect statement about a 90% confidence interval?

A)If we repeatedly draw samples of the same size from the same population, 90% of the resulting confidence intervals will include $\mu$ .
B)There is a 90% probability that the population mean $\mu$ will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).
C)We are 90% confident that our sample mean equals the population mean $\mu$ .
D)90% of the population values will lie within the confidence interval.

Question 42

Increasing the value of 1 - $\alpha$ narrows a confidence interval.

Question 43

Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was:

A)6.62
B)56.34
C)62.96
D)66.15

Question 44

Given a mean of 2.1 and a standard deviation of 0.7, a 90% confidence interval will be 2.1 $\pm$ 0.7.

Question 45

When constructing confidence interval estimate of $\mu$ , doubling the sample size n decreases the width of the interval by half.

Question 46

When constructing confidence interval for a parameter, we generally set the confidence level 1 - $\alpha$ close to 1 (usually between 0.90 and 0.99) because it is the probability that the interval includes the actual value of the population parameter.

Question 47

The letter $\alpha$ in the formula for constructing a confidence interval estimate of the population mean is:

A)the level of confidence.
B)the probability that a particular confidence interval will contain the population mean.
C)the area in the lower tail of the sampling distribution of the sample mean.
D)None of these choices.

Question 48

The width of the confidence interval estimate of the population mean $\mu$ is a function of only two quantities: the population standard deviation $\sigma$ and the sample size n.

Question 49

Suppose that a 95% confidence interval for $\mu$ is given by $\bar { x } \pm 3.25$ . This notation means that, if we repeatedly draw samples of the same size from the same population, 95% of the values of $\bar { x }$ will be such that $\mu$ would lie somewhere between $\bar { x } - 3.25$ and $\bar { x } + 3.25$ .

Question 50

Doubling the population standard deviation $\sigma$ has the effect of doubling the width of the confidence interval estimate of $\mu$ .

Question 51

The lower limit of the 90% confidence interval for $\mu$ , where n = 64, $\bar { x }$ = 70, and $\sigma$ = 20, is 65.89.

Question 52

Other things being equal, as the confidence level increases, the width of the confidence interval increases.

Question 53

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

Question 54

The term 1 - $\alpha$ refers to:

A)the probability that a confidence interval does not contain the population parameter.
B)the confidence level.
C)the level of unbiasedness.
D)the level of consistency.

Question 55

The width of a confidence interval estimate of the population mean increases when the:

A)level of confidence increases
B)sample size decreases
C)value of the population standard deviation increases
D)All of these choices are true.

Question 56

In this chapter you need four values to construct the confidence interval estimate of $\mu$ . They are the sample mean, the sample size, the population standard deviation, and the confidence level.

Question 57

Suppose a sample size of 5 has mean 9.60. If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

Question 58

We cannot interpret the confidence interval estimate of $\mu$ as a probability statement about $\mu$ because the population mean is a fixed quantity.

Question 59

Other things being equal, the confidence interval for the mean will be wider for 99% confidence than for 95% confidence.

Question 60

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 75 to 85. If the confidence level is reduced to 80%, the confidence interval for $\mu$ becomes wider.

Question 61

When estimating the population mean using a confidence interval, the sample mean is in the ____________________ of the interval.

Question 62

A confidence interval is defined as:

A)a point estimate plus or minus a specific confidence level.
B)a lower and upper confidence limit associated with a specific level of confidence.
C)an interval that has a 95% probability of containing the population parameter.
D)a lower and upper confidence limit that has a 95% probability of containing the population parameter.

Question 63

Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?

A)A point estimate of the population mean.
B)The standard error of the sampling distribution of the sample mean.
C)The confidence level.
D)The value of the population mean.

Question 64

Suppose a 95% confidence interval for $\mu$ turns out to be (1,000, 2,100). What does it mean to be 95% confident?

A)In repeated sampling, the population parameter would fall in the resulting interval 95% of the time.
B)95% of the observations in the entire population fall in the given interval.
C)95% of the observations in the sample fall in the given interval.
D)None of these choices.

Question 65

In the formula for a confidence interval for $\mu$ , 1 - $\alpha$ is called the ____________________.

Question 66

The $z _ { \alpha / 2 }$ value for a 95% confidence interval estimate for a population mean $\mu$ is

A)0.95
B)0.025
C)1.65
D)1.96

Question 67

The population mean is a(n) ____________________ but ____________________ quantity.

Question 68

A 99% confidence interval estimate of the population mean $\mu$ can be interpreted to mean:

A)if all possible sample are taken and confidence intervals created, 99% of them would include the true population mean somewhere within their interval.
B)we have 99% confidence that we have selected a sample whose interval does include the population mean.
C)we estimate that the population mean falls between the lower and upper confidence limits, and this type of estimator is correct 99% of the time.
D)All of these choices are true.

Question 69

It is ____________________ to say that a 95% confidence interval means there is a 95% chance that the parameter lies in that confidence interval.

Question 70

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 $\pm$ 2.14. Had $\pm$ equaled 20, the interval estimate would be

A)60.92 $\pm$ 2.14
B)50.92 $\pm$ 12.14
C)101.84 $\pm$ 4.28
D)50.92 $\pm$ 4.28

Question 71

If the confidence level is reduced, the confidence interval:

A)widens.
B)remains the same.
C)narrows.
D)disappears.

Question 72

The smallest number in a confidence interval is abbreviated by ____________________.

Question 73

The larger the confidence level, the:

A)smaller the value of z _{$\alpha$ / 2.}
B)wider the confidence interval.
C)smaller the probability that the confidence interval will contain the population mean.
D)None of these choices.

Question 74

In developing an interval estimate for a population mean, a sample of 50 observations was used. The interval estimate was 19.76 $\pm$ 1.32. Had the sample size been 200 instead of 50, the interval estimate would have been:

A)19.76 $\pm$ .33
B)19.76 $\pm$ .66
C)19.76 $\pm$ 5.28
D)None of these choices.

Question 75

It is desired to estimate the average total compensation of CEOs in the publishing industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000). Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?

A)Yes, and I am sure of that.
B)Yes, and I am 95% confident of that.
C)No, and I am sure of that.
D)No, and I am 95% confident of that.

Question 76

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. In order to correct this problem, you need to:

A)increase the sample size.
B)increase the population standard deviation.
C)increase the level of confidence.
D)increase the sample mean.

Question 77

The confidence ____________________ is the chance that the interval contains the parameter, over repeated sampling.

Question 78

Which of the following conditions does not allow you to use the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ to estimate $\mu$ ?

A)Population is normally distributed and the population variance is known.
B)Population is not normally distributed but n is large; population variance is known.
C)Population has any distribution and n is any size.
D)All of these choices allow you to use the formula.

Question 79

A confidence interval is a probability statement about the ____________________ mean.

Question 80

In the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ , the $\alpha$ / 2 refers to:

A)the probability that the sample mean will not equal the population mean.
B)the probability that the confidence interval will not contain the population mean.
C)the level of confidence.
D)None of these choices.