Deck 8: Estimating the Mean of a Population

Question 1

Calculate the 95% confidence interval for a sample of N = 25 with a mean = 4.06 and standard deviation (s) = 1.37.

A) 95% CI = 4.06 ± .56
B) 95% CI = 4.06 ± .46
C) 95% CI = 4.06 ± .76
D) 95% CI = 4.06 ± 2.33

Answer 1

95% CI = 4.06 ± .56

Question 2

What is the term for the lower and upper boundaries of a confidence interval?

A) point estimate
B) confidence interval
C) confidence limits
D) interval estimate

Answer 2

confidence limits

Question 3

Calculate the 95% confidence interval for a sample of N = 24 with a mean = 102.97 and standard error of the mean = 1.85.

A) 95% CI = 102.97 ± 3.83
B) 95% CI = 102.97 ± 3.17
C) 95% CI = 102.97 ± 5.19
D) 95% CI = 102.97 ± 3.92

Answer 3

95% CI = 102.97 ± 3.83

Question 4

Calculate the 95% confidence interval for a sample of N = 15 with a mean = 3.50 and standard deviation (s) = .80.

A) 95% CI = 3.50 ± .45
B) 95% CI = 3.50 ± .37
C) 95% CI = 3.50 ± .63
D) 95% CI = 3.50 ± 2.36

Question 5

The confidence interval for the mean is ______.

A) a range of values for a variable that has a stated probability of containing an unknown population mean
B) a single value used to estimate an unknown population parameter
C) the lower and upper boundaries of the confidence interval
D) a measure of variability

Question 6

Calculate the 95% confidence interval for a sample of N = 29 with a mean = 52.49 and standard deviation (s) = 11.58.

A) 95% CI = 52.49 ± 4.40
B) 95% CI = 52.49 ± 3.66
C) 95% CI = 52.49 ± 5.94
D) 95% CI = 52.49 ± 4.20

Question 7

Calculate the 95% confidence interval for a sample of N = 30 with a mean = 7.12 and standard deviation (s) = 3.67.

A) 95% CI = 7.12 ± 1.37
B) 95% CI = 7.12 ± 1.14
C) 95% CI = 7.12 ± 1.84
D) 95% CI = 7.12 ± 2.72

Question 8

Calculate the 95% confidence interval for a sample of N = 24 with a mean = 102.97 and standard deviation (s) = 9.05.

A) 95% CI = 102.97 ± 3.83
B) 95% CI = 102.97 ± 3.17
C) 95% CI = 102.97 ± 5.19
D) 95% CI = 102.97 ± 3.92

Question 9

Use the formula to calculate the lower and upper limits of the 95% confidence interval for a sample of N = 12 with a mean = 6.00 and standard error of the mean = 1.15.

A) (3.47, 8.53)
B) (3.93, 8.07)
C) (2.43, 9.57)
D) (2.65, 9.35)

Question 10

What is the term for a single value used to estimate an unknown population parameter?

A) point estimate
B) confidence interval
C) confidence limits
D) interval estimate

Question 11

Calculate the 95% confidence interval for a sample of N = 21 with a mean = 73.51 and standard error of the mean = 2.97.

A) 95% CI = 73.51 ± 6.20
B) 95% CI = 73.51 ± 5.12
C) 95% CI = 73.51 ± 8.45
D) 95% CI = 73.51 ± 5.06

Question 12

Use the formula to calculate the 95% confidence interval for a sample of N = 12 with a mean = 6.00 and standard error of the mean = 1.15.

A) 95% CI = 6.00 ± 2.53
B) 95% CI = 6.00 ± 2.07
C) 95% CI = 6.00 ± 3.57
D) 95% CI = 6.00 ± 3.35

Question 13

Calculate the 95% confidence interval for a sample of N = 21 with a mean = 73.51 and standard deviation (s) = 13.62.

A) 95% CI = 73.51 ± 6.20
B) 95% CI = 73.51 ± 5.12
C) 95% CI = 73.51 ± 8.45
D) 95% CI = 73.51 ± 5.06

Question 14

Use the formula to calculate the 95% confidence interval for a sample of N = 22 with a mean = 9.51 and standard error of the mean = 1.25.

A) 95% CI = 9.51 ± 2.15
B) 95% CI = 9.51 ± 3.52
C) 95% CI = 9.51 ± 2.59
D) 95% CI = 9.51 ± 2.60

Question 15

A point estimate is ______.

A) a measure of variability
B) a single value used to estimate an unknown population parameter
C) the lower boundary of a confidence interval
D) a range or interval of values that has a stated probability of containing an unknown population parameter

Question 16

Confidence limits are ______.

A) a measure of variability
B) single values used to estimate an unknown population parameter
C) the lower and upper boundaries of a confidence interval
D) a range or interval of values that has a stated probability of containing an unknown population parameter

Question 17

Calculate the 95% confidence interval for a sample of N = 15 with a mean = 3.50 and standard error of the mean = .21.

A) 95% CI = 3.50 ± .45
B) 95% CI = 3.50 ± .37
C) 95% CI = 3.50 ± .63
D) 95% CI = 3.50 ± 2.36

Question 18

Calculate the 95% confidence interval for a sample of N = 25 with a mean = 4.06 and standard error of the mean = .27.

A) 95% CI = 4.06 ± .56
B) 95% CI = 4.06 ± .46
C) 95% CI = 4.06 ± .76
D) 95% CI = 4.06 ± 2.33

Question 19

What is the term for a range or interval of values that has a stated probability of containing an unknown population parameter?

A) point estimate
B) confidence interval
C) confidence limits
D) interval estimate

Question 20

A confidence interval is ______.

A) a measure of central tendency
B) a single value used to estimate an unknown population parameter
C) the upper boundary of a confidence interval
D) a range or interval of values that has a stated probability of containing an unknown population parameter

Question 21

Use the formula to calculate the 95% confidence interval for a sample with a mean = 7.00 and a population standard error of the mean = .50.

A) 95% CI = 7.00 ± .98
B) 95% CI = 7.00 ± .83
C) 95% CI = 7.00 ± 1.29
D) 95% CI = 7.00 ± 2.46

Question 22

Calculate the 95% confidence interval for a sample of N = 25 with a mean = 3.74 and a population standard deviation (σ) = 6.00.

A) 95% CI = 3.74 ± 2.35
B) 95% CI = 3.74 ± 1.98
C) 95% CI = 3.74 ± 3.10
D) 95% CI = 3.74 ± 3.16

Question 23

Which of the following statements would be the correct way to state a conclusion regarding a 95% confidence interval?

A) There is a .05 probability that the population mean is between 35,422 and 41,566.
B) There is a .95 probability that the interval of 35,422 to 41,566 contains the population mean.
C) There is a .95 probability that the population mean is between 35,422 and 41,566.
D) There is a .05 probability that the interval of 35,422 to 41,566 contains the population mean.

Question 24

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 29 with a mean = 52.49 and standard error of the mean = 2.15.

A) (48.29, 56.69)
B) (48.83, 56.15)
C) (46.55, 58.43)
D) (48.09, 56.89)

Question 25

Calculate the 95% confidence interval for a sample of N = 28 with a mean = 15.86 and a population standard deviation (σ) = 10.00.

A) 95% CI = 15.86 ± 3.12
B) 95% CI = 15.86 ± 3.70
C) 95% CI = 15.86 ± 4.88
D) 95% CI = 15.86 ± 3.85

Question 26

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 25 with a mean = 10.50 and standard deviation (s) = 4.16.

A) (8.83, 12.17)
B) (8.78, 12.22)
C) (8.17, 12.83)
D) (7.59, 13.41)

Question 27

Calculate the 95% confidence interval for a sample of N = 17 with a mean = 12.42 and a population standard deviation (σ) = 5.00.

A) 95% CI = 12.42 ± 2.37
B) 95% CI = 12.42 ± 2.00
C) 95% CI = 12.42 ± 3.12
D) 95% CI = 12.42 ± 3.17

Question 28

Calculate the 95% confidence interval for a sample with a mean = 117.52 and a population standard error of the mean = 5.57.

A) 95% CI = 117.52 ± 10.92
B) 95% CI = 117.52 ± 9.19
C) 95% CI = 117.52 ± 14.37
D) 95% CI = 117.52 ± 7.53

Question 29

Calculate the 95% confidence interval for a sample with a mean = 15.86 and a population standard error of the mean = 1.89.

A) 95% CI = 15.86 ± 3.70
B) 95% CI = 15.86 ± 3.12
C) 95% CI = 15.86 ± 4.88
D) 95% CI = 15.86 ± 3.85

Question 30

Calculate the 95% confidence interval for a sample with a mean = 57.28 and a population standard error of the mean = 3.27.

A) 95% CI = 57.28 ± 6.41
B) 95% CI = 57.28 ± 5.40
C) 95% CI = 57.28 ± 8.44
D) 95% CI = 57.28 ± 5.23

Question 31

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 25 with a mean = 4.06 and standard error of the mean = .27.

A) (3.50, 4.62)
B) (3.60, 4.52)
C) (3.30, 4.82)
D) (1.73, 6.39)

Question 32

Calculate the 95% confidence interval for a sample with a mean = 12.67 and a population standard error of the mean = .98.

A) 95% CI = 12.67 ± 1.61
B) 95% CI = 12.67 ± 1.92
C) 95% CI = 12.67 ± 2.28
D) 95% CI = 12.67 ± 2.52

Question 33

Calculate the 95% confidence interval for a sample with a mean = 2.50 and a population standard error of the mean = .20.

A) 95% CI = 2.50 ± .39
B) 95% CI = 2.50 ± .33
C) 95% CI = 2.50 ± .52
D) 95% CI = 2.50 ± 2.16

Question 34

Calculate the 95% confidence interval for a sample with a mean = 249.60 and a population standard error of the mean = 9.13.

A) 95% CI = 249.60 ± 17.89
B) 95% CI = 249.60 ± 15.06
C) 95% CI = 249.60 ± 23.56
D) 95% CI = 249.60 ± 11.09

Question 35

Calculate the 95% confidence interval for a sample of N = 30 with a mean = 249.60 and a population standard deviation (σ) = 50.00.

A) 95% CI = 249.60 ± 23.56
B) 95% CI = 249.60 ± 15.06
C) 95% CI = 249.60 ± 17.89
D) 95% CI = 249.60 ± 11.09

Question 36

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 28 with a mean = 16.39 and standard error of the mean = .91.

A) (14.52, 18.26)
B) (14.84, 17.94)
C) (13.87, 18.91)
D) (13.43, 19.35)

Question 37

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 24 with a mean = 102.97 and standard error of the mean = 1.85.

A) (99.14, 106.80)
B) (99.8, 106.14)
C) (97.78, 108.16)
D) (99.05, 106.89)

Question 38

Which of the following statements would be the correct way to state a conclusion regarding a 95% confidence interval?

A) There is a 95% probability that the population mean is between 131.65 and 135.78.
B) There is a .95 probability that the population mean is between 131.65 and 135.78.
C) There is a .95 probability that the interval of 131.65 and 135.78 contains the population mean.
D) There is a 95% probability that the interval of 131.65 and 135.78 contains the population mean.

Question 39

Calculate the lower and upper limits of the 95% confidence interval for a sample with a mean = 2.50 and a population standard error of the mean = .20.

A) (2.11, 2.89)
B) (2.17, 2.83)
C) (1.98, 3.02)
D) (.34, 4.66)

Question 40

Calculate the lower and upper limits of the 95% confidence interval for a sample with a mean = 7.00 and a population standard error of the mean = .50.

A) (6.02, 7.98)
B) (6.18, 7.83)
C) (5.71, 8.29)
D) (4.54, 9.46)

Question 41

The distribution of sample means for larger samples is more closely clustered around the population mean, with less ______ among sample means.

A) confidence
B) significance
C) similarity
D) variability

Question 42

When a sample size is decreased, the confidence interval for the mean is then ______.

A) narrowed
B) widened
C) more significant
D) less significant

Question 43

The ______ the sample, the less confidence a research has that the sample mean estimates the unknown population mean μ, and the ______ the confidence interval around the sample mean.

A) larger; smaller
B) larger; larger
C) smaller; larger
D) smaller; smaller

Question 44

What is the relationship between the size of a sample and the width of the confidence interval for the mean?

A) The smaller the sample size, the narrower the confidence interval for the mean.
B) The larger the sample size, the narrower the confidence interval for the mean.
C) The larger the sample size, the wider the confidence interval for the mean.
D) The size of the sample has no influence on the width of the confidence interval for the mean.

Question 45

Calculate the lower and upper limits of the 95% confidence interval for a sample with a mean = 57.28 and a population standard error of the mean = 3.27.

A) (40.87, 63.69)
B) (51.88, 62.68)
C) (48.84, 65.72)
D) (52.05, 62.51)

Question 46

When drawing a conclusion about the 95% confidence interval with a known population standard deviation, a researcher would state that there is a ______.

A) .95 probability that a confidence interval contains the median score for the population
B) 95% probability that a confidence interval contains the mean score for the population
C) .95 probability that a confidence interval contains the mean score for the population
D) .05 probability that a confidence interval contains the mean score for the population

Question 47

A sample size of ______ would have the widest confidence interval for the mean.

A) N = 200
B) N = 250
C) N = 300
D) N = 350

Question 48

The distribution of sample means for relatively ______ samples is closely clustered around the population mean, with less variability among sample means.

A) large
B) small
C) normally distributed
D) skewed

Question 49

The ______ the sample, the more confidence a researcher has that the sample mean estimates the unknown population mean μ, and the ______ the confidence interval around the sample mean.

A) larger; larger
B) smaller; smaller
C) smaller; larger
D) larger; smaller

Question 50

Calculate the lower and upper limits of the 95% confidence interval for a sample with a mean = 28.59 and a population standard error of the mean = 2.29.

A) (24.10, 33.08)
B) (24.81, 32.37)
C) (22.68, 34.50)
D) (24.34, 32.84)

Question 51

The relationship between sample size and the width of a confidence interval may be explained by the concept of ______.

A) z score
B) point estimates
C) sampling error
D) descriptive statistics

Question 52

The larger the sample size, the ______ the confidence interval for the mean.

A) narrower
B) wider
C) broader
D) more significant

Question 53

When a sample size is increased, the confidence interval for the mean is then ______.

A) more significant
B) widened
C) narrowed
D) less significant

Question 54

Calculate the lower and upper limits of the 95% confidence interval for a sample with a mean = 12.67 and a population standard error of the mean = .98.

A) (11.06, 14.28)
B) (10.75, 14.59)
C) (10.39, 14.95)
D) (10.15, 15.19)

Question 55

If a researcher were to increase the sample size from 100 to 200, the confidence interval for the mean would be ______.

A) widened
B) narrowed
C) unchanged
D) more normally distributed

Question 56

Researchers have more confidence that the sample mean estimates the unknown population mean when their sample is ______.

A) centralized
B) significant
C) larger
D) smaller

Question 57

The ______ the desired width of a confidence interval, the ______ the necessary sample size.

A) larger; larger
B) smaller; smaller
C) larger; smaller
D) smaller; larger

Question 58

There is a .95 probability that a confidence interval contains the ______ score for the population.

A) median
B) mean
C) standard deviation
D) variance

Question 59

______ samples have ______ value for the standard error of the mean, which in turn narrows the width of the confidence interval.

A) Larger; larger
B) Smaller; smaller
C) Larger; smaller
D) Smaller; larger

Question 60

A sample of size ______ would have the narrowest confidence interval for the mean.

A) N = 140
B) N = 200
C) N = 300
D) N = 425

Question 61

When a researcher moves from a 95% confidence level to a 99% confidence level, the confidence interval for the mean becomes ______.

A) wider
B) normally distributed
C) statistically significant
D) narrower

Question 62

Which of the following affects the width of a confidence interval?

A) whether the population standard deviation is known
B) the sample mean
C) the desired level of confidence
D) the population mean

Question 63

If a researcher decreases the confidence level from 99% to 90%, the confidence interval for the mean is ______.

A) widened
B) unchanged
C) narrowed
D) restricted

Question 64

For a variable with = 15.00, how large should the sample be for a desired 95% confidence interval width of 6?

A) 10
B) 24
C) 96
D) 576

Question 65

Which confidence interval is the narrowest?

A) 99.9%
B) 99%
C) 95%
D) 90%

Question 66

If a researcher chooses a confidence level greater than the 95%, which of the following will occur?

A) a smaller confidence interval that contains the population mean
B) a larger confidence interval that contain the population mean
C) a loss of precision in estimating the sample mean
D) a loss of precision in estimating the population mean

Question 67

For a variable with = 25.00, how large should the sample be for a desired 95% confidence interval width of 15?

A) 7
B) 11
C) 43
D) 121

Question 68

Use the formula to calculate the 90% confidence interval for a sample of N = 12 with a mean = 4.00 and standard error of the mean = .58.

A) 90% CI = 4.00 ± 1.04
B) 90% CI = 4.00 ± 1.80
C) 90% CI = 4.00 ± 2.38
D) 90% CI = 4.00 ± 1.28

Question 69

For a variable with = 333.00, how large should the sample be for a desired 95% confidence interval width of 100?

A) 13
B) 43
C) 170
D) 1849

Question 70

For a variable with = 5.81, how large should the sample be for a desired 95% confidence interval width of 2?

A) 11
B) 32
C) 130
D) 1024

Question 71

When a researcher increases the confidence level from 95% to 99%, the wider interval implies ______.

A) increased precision in estimating the population mean
B) a lower confidence that the interval contains the population mean
C) a loss of precision in estimating the sample mean
D) decreased precision in estimating the population mean

Question 72

The ______ the desired level of confidence, the ______ the confidence interval for the mean.

A) higher; wider
B) lower; narrower
C) higher; narrower
D) lower; wider

Question 73

Which confidence interval is the widest?

A) 99.9%
B) 99%
C) 95%
D) 90%

Question 74

When a researcher moves from a 95% confidence level to a 90% confidence level, the confidence interval for the mean becomes ______.

A) wider
B) normally distributed
C) statistically significant
D) narrower

Question 75

When a researcher moves from a 90% confidence level to a 95% confidence level, the width of the confidence interval for the mean is ______.

A) increased
B) unchanged
C) less significant
D) decreased

Question 76

For a variable with = 175.00, how large should the sample be for a desired 95% confidence interval width of 50?

A) 14
B) 47
C) 188
D) 2209

Question 77

For a variable with = 3.50, how large should the sample be for a desired 95% confidence interval width of 1.50?

A) 9
B) 21
C) 84
D) 441

Question 78

If a researcher chooses a confidence level less than the 95%, which of the following occurs?

A) a smaller confidence interval that contains the population mean
B) a larger confidence interval that contain the population mean
C) a loss of precision in estimating the sample mean
D) a loss of precision in estimating the population mean

Question 79

The ______ the desired width of a confidence interval, the ______ the necessary sample size.

A) larger; larger
B) smaller; smaller
C) larger; smaller
D) smaller; larger

Question 80

The ______ the desired level of confidence, the ______ the confidence interval for the mean.

A) higher; narrower
B) lower; narrower
C) lower; wider
D) lower; higher