CHAPTER 8—INTERVAL ESTIMATION

MULTIPLE CHOICE

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

ANS: B PTS: 1 TOP: Interval Estimation

2. When s is used to estimate s, 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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

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.

ANS: B PTS: 1 TOP: Interval Estimation

8. For the interval estimation of m when s 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

ANS: A PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

15. In order to use the normal distribution for interval estimation of m when s 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

ANS: B PTS: 1 TOP: Interval Estimation

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 (m).

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.

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: A PTS: 1 TOP: Interval Estimation

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 m, 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

ANS: D PTS: 1 TOP: Interval Estimation

19. The z value for a 97.8% confidence interval estimation is

a. / 2.02
b. / 1.96
c. / 2.00
d. / 2.29

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

22. For which of the following values of P is the value of P(1 - P) maximized?

a. / P = 0.99
b. / P = 0.90
c. / P = 0.01
d. / P = 0.50

ANS: D PTS: 1 TOP: Interval Estimation

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 m

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

ANS: A PTS: 1 TOP: Interval Estimation

24. Using an a = 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

ANS: B PTS: 1 TOP: Interval Estimation

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 m
d. / degrees of freedom minus 1

ANS: A PTS: 1 TOP: Interval Estimation

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.

ANS: C PTS: 1 TOP: Interval Estimation

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

ANS: A PTS: 1 TOP: Interval Estimation

28. In general, higher confidence levels provide

a. / wider confidence intervals
b. / narrower confidence intervals
c. / a smaller standard error
d. / unbiased estimates

ANS: A PTS: 1 TOP: Interval Estimation

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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

32. A sample of 20 items from a population with an unknown s is selected in order to develop an interval estimate of m. 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 s.
d. / The sample must have a normal distribution.

ANS: D PTS: 1 TOP: Interval Estimation

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 m 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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: A PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: B PTS: 1 TOP: Interval Estimation

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

ANS: C PTS: 1 TOP: Interval Estimation

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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: A PTS: 1 TOP: Interval Estimation

42. The following random sample from a population whose values were normally distributed was collected.

10 / 8 / 11 / 11

The 95% confidence interval for m 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

ANS: B PTS: 1 TOP: Interval Estimation

43. The following random sample from a population whose values were normally distributed was collected.

10 / 12 / 18 / 16

The 80% confidence interval for m 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

ANS: D PTS: 1 TOP: Interval Estimation

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 n(1-p) 5.

ANS: D PTS: 1 TOP: Interval Estimation

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

ANS: A PTS: 1 TOP: Interval Estimation

46. In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is