Stat 511 Quiz

13. A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of , 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

A

17. 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 a. becomes narrower b. becomes wider c. does not change d. becomes 0.1

A

19. 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 d. degrees of freedom minus 1

A

21. 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

A

22. In general, higher confidence levels provide a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates

A

6. 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

A

1. 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

B

10. 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

B

15. The t critical 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

B

16. 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

B

18. Using an = 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

B

26. 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

B

5. 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.

B

7. 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

B

8. 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

B

11. 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

C

2. 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

C

20. 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.

C

24. 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

C

3. 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

C

4. 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

C

12. 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.

D

14. The z critical value for a 97.8% confidence interval estimation is a. 2.02 b. 1.96 c. 2.00 d. 2.29

D

23. 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

D

25. 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 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

D

27. 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

D

28. 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

D

9. 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

D