Deck 11: Estimation: Describing a Single Population

Question 1

Which of the following best describes an interval estimator? $\alpha$$\begin{array}{|l|l|}\hline A&\text { An interval estimator is the same as a point estimator.}\\\hline B&\text {An interval estimator is an interval that draws inferences about a }\\&\text {population based on a sample statistic. }\\\hline C&\text { An interval estimator can only be done for the population mean.}\\\hline D&\text { An interval estimator can only be done for the population proportion.}\\\hline \end{array}$

Answer 1

B

Question 2

In developing an interval estimate for a population mean, the interval estimate 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:

Answer 2

D

Question 3

Which of the following best describes an unbiased estimator?

Answer 3

C

Question 4

A point estimate is defined as:

Question 5

The degrees of freedom used to find the t_/2 for a confidence interval for the population mean?

Question 6

If the Student t distribution is incorrectly used instead of the Standard normal distribution when finding the confidence interval for the population mean, and the population variance was known, what will happen to the width of the confidence interval?

Question 7

The z value for a 95% confidence interval estimate is:

Question 8

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

Question 9

Which of the following is the width of the confidence interval for the population mean?

Question 10

A random sample of 64 observations has a mean of 30. The population variance is assumed to be 9. The 85.3% confidence interval estimate for the population mean (to the third decimal place) is:

Question 11

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

Question 12

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval $\mu$ : $\begin{array}{|l|l|}\hline A&\text {becomes wider. }\\\hline B&\text {remains the same. }\\\hline C&\text {becomes narrower. }\\\hline D&\text {None of these choices are correct. }\\\hline \end{array}$

Question 13

In developing an interval estimate at 87.4% for a population mean, the value of z to use is:

Question 14

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 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been: $\begin{array}{|l|l|}\hline \text { A. } & 60.92 \pm 2.14 . \\\hline \text { B. } & 50.92 \pm 12.14 \\\hline \text { C. } & 101.84 \pm 4.28 \\\hline \text { D. } & 50.92 \pm 4.28 . \\\hline\end{array}$

Question 15

Which of the following statements are correct?

Question 16

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown?

Question 17

Which of the following statements is (are) correct?

Question 18

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

Question 19

Which of the following statistical distributions is used when estimating the population mean when the population variance is known?

Question 20

A 90% confidence interval estimate of the population mean $\mu$ can be interpreted to mean that: $\begin{array}{|l|l|}\hline A&\text {if we repeatedly draw samples of the same size from the same population, \( 90 \% \) of the }\\&\text { values of the sample means \( \bar{x} \) will result in a}\\&\text { confidence interval that includes the population mean.}\\\hline B&\text { there is a \( 90 \% \) probability that the population mean will lie between the lower confidence}\\&\text { limit (LCL) and the upper confidence limit (UCL). }\\\hline C&\text {we are \( 90 \% \) confident that we have selected a sample whose range of values does }\\&\text {not contain the population mean. }\\\hline D&\text { We are \( 90 \% \) confident that \( 10 \% \) the values of the sample means \( \bar{x} \) will result in a }\\&\text {confidence interval that includes the population mean. }\\\hline \end{array}$

Question 21

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula?

Question 22

Which of the following is true about the t-distribution? $\begin{array}{|l|l|}\hline A&\text { It approaches the normal distribution as the number of degrees of freedom increases.}\\\hline B&\text {It assumes that the population is normally distributed. }\\\hline C&\text { It is more spread out than the standard normal distribution.}\\\hline D&\text { All of these choices are correct.}\\\hline \end{array}$

Question 23

As the number of degrees of freedom for a t-distribution increases:

Question 24

Which of the following statements is (are) true? $\begin{array}{|l|l|}\hline A&\text { The sample mean is relatively more efficient than the sample median. }\\\hline B&\text { The sample median is relatively more efficient than the sample mean.}\\\hline C&\text { The sample variance is relatively more efficient than the sample variance.}\\\hline D&\text {All of these choices are correct. }\\\hline \end{array}$

Question 25

In the formula , the refers to:

Question 26

For statistical inference about the mean of a single population when the population standard deviation is unknown, the number of degrees for freedom for the t-distribution is equal to n - 1 because we lose one degree of freedom by using the:

Question 27

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

Question 28

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of:

Question 29

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion , we:

Question 30

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

Question 31

The objective of estimation is to determine the approximate value of:

Question 32

The smaller the level of confidence used in constructing a confidence interval estimate of the population mean, the:

Question 33

The problem with relying on a point estimate of a population parameter is that:

Question 34

A confidence interval is defined as:

Question 35

The sample variance is an unbiased estimator of the population variance when the denominator of is:

Question 36

The student t-distribution approaches the normal distribution as the:

Question 37

A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance would be:

Question 38

A robust estimator is one that:

Question 39

Which of the following statements is false? $\begin{array}{|l|l|}\hline A&\text {The \( t \)-distribution is symmetric about zero. }\\\hline B&\text {The \( t \)-distribution is more spread out than the standard normal distribution. }\\\hline C&\text { As the number of degrees of freedom gets smaller, the \( t \)-distribution's}\\&\text {dispersion gets smaller. }\\\hline D&\text {The \( t \)-distribution is mound-shaped. }\\\hline \end{array}$

Question 40

Which of the following assumptions must be true in order to use the formula $\bar { x } \pm z _ {\alpha / 2 } \sigma / \sqrt { n }$ to find a confidence interval estimate of the population mean? $\begin{array}{|l|l|}\hline A&\text {The population variance is known. }\\\hline B&\text { The population mean is known.}\\\hline C&\text { The population is normally distributed.}\\\hline D&\text {The confidence level is greater than \( 90 \% \). }\\\hline \end{array}$

Question 41

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

Question 42

An unbiased estimator of a population parameter is an estimator whose expected value is equal to the population parameter to be estimated.

Question 43

If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be:

Question 44

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 45

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

Question 46

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

Question 47

An interval estimate is a range of values within which the actual value of a population parameter $\mu$ falls.

Question 48

From a sample of 300 items, 15 are defective. The point estimate of the population proportion defective will be:

Question 49

A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:

Question 50

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

Question 51

After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be:

Question 52

The sample proportion is a biased estimator of the population proportion.

Question 53

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

Question 54

A random sample of size n has been selected from a normally distributed population whose standard deviation is s. In estimating an interval for the population mean, the t-distribution should be used instead of the z-test if:

Question 55

A sample of size 300 is to be taken at random from an infinite population. Given that the population proportion is 0.70, the probability that the sample proportion will be smaller than 0.75 is:

Question 56

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either:

Question 57

The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is:

Question 58

The probability that a confidence interval includes the parameter of interest is either 1 or 0.

Question 59

The sample standard deviation is an unbiased estimator of the population standard deviation.

Question 60

An interval estimate is an estimate of the range for a population parameter.

Question 61

The difference between the sample statistic and actual value of the population parameter is the percentage of the confidence interval.

Question 62

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

Question 63

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 ± 2.50. Had $\sigma$ equalled 16, the interval estimate would have been 100 ± 5.0.

Question 64

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 we would like to be reasonably confident that the interval includes the actual value of the population parameter.

Question 65

The lower and upper limits of the 68.26% confidence interval for the population mean $\mu$ , given that n = 64, $\bar { x }$ = 110 and $\sigma$ = 8, are 109 and 111, respectively.

Question 66

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

Question 67

The sample proportion $\hat { p }$ is a consistent estimator of the population proportion p because it is unbiased and the variance of $\hat { p }$ is p(1 - p)/n, which grows smaller as n grows larger.

Question 68

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

Question 69

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

Question 70

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

Question 71

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

Question 72

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 73

The range of a confidence interval is a measure of the expected sampling error.

Question 74

The sample mean is an unbiased estimator of the population mean $\mu$ , and (when sampling from a normal population) the sample median is also an unbiased estimator of $\mu$ . However, the sample mean is relatively more efficient than the sample median.

Question 75

The percentage of the confidence interval relies on the significance level. $\alpha$

Question 76

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is n - 1.

Question 77

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 narrower.

Question 78

The sample mean $\bar { x }$ is a consistent estimator of the population mean $\mu$ .

Question 79

The width of a confidence interval increases as the level of significance increases.

Question 80

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.