Deck 12: Confidence Interval Versus Point Estimation

Question 1

A point estimate

A) is based on population data.
B) is a single value.
C) is a range of values.
D) has a specified degree of confidence.

Answer 1

B

Question 2

Sample statistics are not expected to predict with certainty the values of the population because of

A) sampling error.
B) experimenter error.
C) confidence error.
D) interval error.

Answer 2

A

Question 3

A sample mean used to predict a population mean is an example of a

A) sample valuation.
B) sample forecast.
C) confidence interval.
D) point estimate.

Answer 3

D

Question 4

Which of the following is NOT true of confidence intervals?

A) They take sampling error into consideration.
B) They are expected to include a population parameter.
C) They include a range of values.
D) They are more specific than point estimates.

Question 5

Which of the following is NOT true of point estimates?

A) They are based on sample data.
B) They are used to estimate the parameters of a population.
C) They include adjustments for standard error.
D) They are more specific than confidence intervals.

Question 6

Point estimates involve _______ values and are _______ specific than confidence intervals.

A) a range of; less
B) single; more
C) a range of; more
D) single; less

Question 7

To determine the point estimate of a population parameter, use

A) the obtained sample values with an adjustment for standard error.
B) the denominator of the t test.
C) the numerator of the t test.
D) the appropriate confidence interval.

Question 8

For a one-sample t test, the point estimate would be

A) M
B) μ
C) M_D
D) μ_D

Question 9

For an independent samples t test, the point estimate would be

A) μ₁ - μ₂
B) M₁ - M₂
C)
D) M_D

Question 10

For a repeated measures t test, the point estimate would be

A) μ₁ - μ₂
B) M₁ - M₂
C) μ_D
D) M_D

Question 11

Confidence intervals are _______ specific than point estimates and involve _______ values.

A) more; single
B) less; a range of
C) more; a range of
D) less; single

Question 12

Which of the following components is not needed for calculating the lower and upper limits of a confidence interval?

A) an obtained statistic
B) a population parameter
C) a t-value
D) the estimated standard error

Question 13

If we want to establish a 99% confidence interval for the population mean, then our interval would fail to capture μ _____ percent of the time.

A) 1
B) 10
C) 100
D) .5

Question 14

Which is the correct formula for the upper limit of a confidence interval for a one-sample t test?

A) M + t(s_M)
B) μ + t(s_M)
C) M_D + t (s_MD)
D) μ_D + t (s_MD)

Question 15

Which is the correct formula for the lower limit of a confidence interval for an independent samples t test?

A) M_D - t (s_MD)
B) μ_D - t (s_MD)
C) (μ₁ - μ₂) - t (s_M₁-M₂)
D) (M₁ - M₂) - t (s_M₁-M₂)

Question 16

Which is the correct formula for the lower limit of a confidence interval for a repeated measures t test?

A) M_D - t (s_MD)
B) μ_D - t (s_MD)
C) (μ₁ - μ₂) - t (s_M₁-M₂)
D) (M₁ - M₂) - t (s_M₁-M₂)

Question 17

Given the scores 10, 12, 15, and 20, what is the point estimate for μ?

A) 57
B) 14.25
C) 19
D) ±10

Question 18

The scores for group one in a study are 4, 5, 6, and 7. The scores for group two are 8, 9, 10, 11, and 12. What would the point estimate be for an independent samples t test?

A) -4.50
B) +4.50
C) +8.00
D) 10.29

Question 19

The pre-test scores for a repeated measures test were 6, 8, 10, and 9. The post-test scores for the same participants in the same order were 8, 10, 11, and 12. What would be point estimate be for μ_D?

A) -1.75
B) +1.75
C) +2.00
D) -2.00

Question 20

If we wanted to estimate a 90% confidence interval for a one-sample t test with a sample of n = 18, what t-values would we use?

A) ±1.740
B) ±1.734
C) ±2.101
D) ±2.110

Question 21

If we wanted to estimate a 98% confidence interval for an independent samples t test with sample sizes of n = 11 and n = 12, what t-values would we use?

A) ±2.819
B) ±2.831
C) ±2.518
D) ±2.508

Question 22

If we wanted to estimate an 80% confidence interval for a two-sample repeated measures t test with a sample size of n = 23, what t values would we use?

A) ±1.323
B) ±1.721
C) ±1.717
D) ±1.321

Question 23

If we have established a 99% confidence interval for μ of 40 to 60, what would be the correct interpretation?

A) 99% of sample means would fall between 40 and 60.
B) 99% of population means would fall between 40 and 60.
C) We can be 99% confident that μ would be between 40 and 60.
D) We can be 99% confident that M would be between 40 and 60.

Question 24

If we were conducting an independent samples t test, a point estimate would be used to estimate

A) the sample mean difference.
B) the population mean difference.
C) the difference between sample means.
D) the difference between population means.

Question 25

If we were conducting repeated measures t test, a point estimate would be used to estimate

A) the sample mean difference.
B) the population mean difference.
C) the difference between sample means.
D) the difference between population means.

Question 26

A study was conducted to determine the effectiveness of interval training (alternating between walking and running at a fast pace) on running speed. A sample of n = 9 runners improved their speed on 5K runs after the training by an average of M_D = 1.58 minutes with s_D = .61. What would the point estimate of the mean difference be in the population?

A) 1.58
B) .1756
C) .1975
D) 7.77

Question 27

A study was conducted to determine the effectiveness of interval training (alternating between walking and running at a fast pace) on running speed. A sample of n = 9 runners improved their speed on 5K runs after the training by an average of M_D = 1.58 minutes with s_D = .61. If we want to construct a 90% confidence interval for the population mean difference, what t-values should be used.

A) ±2.365
B) ±2.306
C) ±1.895
D) ±1.860

Question 28

A study was conducted to determine the effectiveness of interval training (alternating between walking and running at a fast pace) on running speed. A sample of n = 9 runners improved their speed on 5K runs after the training by an average of M_D = 1.58 minutes with s_D = .61. The values for a 95% confidence interval for μ_D would be

A) .20 to 3.18
B) .17 to 2.99
C) 1.13 to 2.04
D) .14 to 3.02

Question 29

When level of confidence is ______, the range of values becomes _______.

A) decreased; broader
B) increased; broader
C) increased; more specific
D) decreased; less specific

Question 30

As compared to point estimates, confidence intervals are

A) less specific but we can have greater confidence that they will include the population values.
B) more specific and we have greater confidence that they will include the population values.
C) less specific and we have less confidence that they will include the population values.
D) more specific but we have less confidence that they will include the population values.

Question 31

When the level of confidence is increased, the range of values ______ and becomes ________ specific.

A) narrows; less
B) narrows; more
C) broadens; more
D) broadens; less

Question 32

Explain the difference between a point estimate and a confidence interval.

Question 33

If we wanted to make a point estimate for μ, what statistic would we use?

Question 34

If we wanted to make a point estimate for μ₁ - μ₂, what statistic would we use?

Question 35

If we wanted to make a point estimate for μ_D, what statistic would we use?

Question 36

What is the relationship between level of confidence and the width of the confidence interval?

Question 37

Based on the summary data below, construct a 90% confidence interval for μ.
M = 50
n = 15
s_M = 3

Question 38

Based on the summary data below, construct an 80% confidence interval forμ₁ - μ₂.
M₁ = 70 with n₁ = 18
M₂ = 64 with n₂ = 15

Question 39

Based on the summary data below, construct a 98% confidence interval for μ_D.
M_D = 11
n = 12

Question 40

Given the scores 31, 42, 29, and 35, what is the point estimate for μ?

Question 41

Group One scores 9, 12, 8, 15, and 11. Group Two scores 23, 18, 14, 20, 19, and 17. What is the point estimate for μ₁ - μ₂?

Question 42

The scores before a treatment intervention were 10, 8, 11, 9, and 8. The scores after the intervention were 6, 5, 6, 3, and 5, respectively. What is the point estimate for μ_D?

Question 43

Based on the summary data below, construct a 95% confidence interval forμ.
M = 25
n = 12
SS = 200

Question 44

Based on the summary data below, construct a 99% confidence interval for μ₁ -μ₂.
M₁ = 62 with n₁ = 14 and SS₁ = 501
M₂ = 55 with n₂ = 16 and SS₂ = 441

Question 45

Based on the summary data below, construct a 98% confidence interval for μ_D.
M_D = 8
n = 24
SS_D = 893