Deck 6: Estimation and Confidence Intervals

Question 1

A single "best guess" from a sample as an estimate of a parameter is a ______.

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

Answer 1

C

Question 2

Which of the following is an example of a point estimate for $\mu$ ?

A) x̄
B) x̄ - $\mu$
C) Sx̄
D) none of these

Answer 2

x̄

Question 3

You randomly draw a sample of n = 20 from a population. The sample has a mean of 10. What is the point estimate of $\mu$ ?

A) 20
B) 10
C) 0.5
D) impossible to determine

Answer 3

10

Question 4

You randomly draw a sample of 50 organizations from a population of organizations where x̄ = 75. What is the point estimate of $\mu$ ?

A) 1.25
B) 50
C) 75
D) impossible to determine

Question 5

Your point estimate is likely to be more accurate if ______.

A) the standard error is large
B) the standard deviation is large
C) the sample size is large
D) all of these

Question 6

A researcher has identified in the average salary for a sample of his employees. If he wants to make general conclusions about the population of employees, what is that average salary?

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

Question 7

Which of the following situations would provide the most accurate estimate of $\mu$ ?

A) n = 10; s = 50
B) n = 10; s = 5
C) n = 100; s = 50
D) n = 100; s = 5

Question 8

An advantage to using interval estimates instead of point estimates is ______.

A) interval estimates provide more information than point estimates
B) interval estimates are easier to calculate than point estimates
C) interval estimates are easier to interpret that point estimates
D) all of these

Question 9

A range of values in which we'd expect sample statistics to fall given a particular sample size, particular parameter, and particular confidence level, would be considered a ______.

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

Question 10

In order to calculate the boundaries of a confidence interval, you must know ______.

A) the sample size
B) a point estimate
C) confidence level
D) all of these

Question 11

If you compute an interval with a 99% confidence level, this means that 99% of sample means drawn from the population will be ______.

A) important
B) accurate
C) between the bounds
D) greater than zero

Question 12

When calculating a confidence interval, you find a lower bound of 10 and an upper bound of 15. Choose the correct interpretation of this interval.

A) 95% of samples of the same size drawn from the population will fall beyond 10 and 15.
B) 95% of samples of the same size drawn from the population will fall between 10 and 15.
C) There is a 95% chance that the population mean is between 10 and 15.
D) There is a 95% chance that our sample mean accurately represents the population mean.

Question 13

You should use a 100% confidence level when ______.

A) you want to provide the most conservative estimate of the parameter
B) you want to provide the most representative estimate of the parameter
C) you want to provide the most accurate estimate of the parameter
D) none of these; never

Question 14

You calculate a 95% confidence interval with bounds 2.5 and 7. Which of these is an appropriate way to state that confidence interval?

A) CI₉₅ = [7.0, 2.5]
B) CI₉₅ = [2.5, 7.0]
C) CI₉₅ = (7.0, 2.5)
D) CI₉₅ = (2.5, 7.0)

Question 15

You randomly draw a sample of n = 25 from a population where $\sigma$ = 3. Which is the appropriate formula for the bounds of a 95% confidence interval?

A) $\bar{x} \pm 1.960 * 0.6$
B) $\bar{x} \pm 1.645 * 0.6$
C) $\bar{x} \pm 1.960 * 0.12$
D) $\bar{x} \pm 1.645 * 0.12$

Question 16

You randomly draw a sample of n = 16 where $\sigma$ = 4. If the sample mean is 1, which of the following are the bounds of a 95% confidence interval?

A) -2.96, .96
B) -.96, 2.96
C) -14.68, 16.68
D) -16.68, 14.68

Question 17

You randomly draw a sample of n = 25 where $\sigma$ ² = 100. If the sample mean is 10, which of the following are the bounds of a 95% confidence interval?

A) 6.08, 13.92
B) -29.2, 49.2
C) -49.2, 29.2
D) -38.2, 40.2

Question 18

You randomly draw a sample of n = 8 where $\sigma$ = 8. If the sample mean is -10, which of the following are the bounds of a 99% confidence interval?

A) -15.54, -4.46
B) -11.96, -8.04
C) -12.58, -7.42
D) -17.28, -2.72

Question 19

You randomly draw a sample of n = 12 where $\sigma$ ² = 40. If the sample mean is 5, which of the following are the bounds of a 99% confidence interval?

A) -24.73, 34.73
B) 0.30, 9.70
C) 1.42, 8.58
D) -17.63, 27.63

Question 20

When calculating the confidence interval, if the population standard deviation is not known, it is replaced in the confidence interval boundary formula with ______.

A) the sample range
B) the sample standard deviation
C) n - 1
D) A confidence interval should not be computed if the population standard deviation is unknown.

Question 21

When n > 30, you would expect ______.

A) the z-distribution and t-distribution to be dissimilar
B) the z-distribution and t-distribution to be similar
C) the z-distribution and t-distribution to be identical
D) none of these

Question 22

You randomly select a sample of n = 16 organizations. For this sample, the standard deviation is 8. To calculate a 99% confidence interval, which of the following formulas would you use?

A) x̄ ± 1.753 * 2
B) x̄ ± 2.131 * 2
C) x̄ ± 1.753 * 0.5
D) x̄ ± 2.131 * 0.5

Question 23

You randomly select a sample of n = 30. What are the degrees of freedom associated with a confidence interval of the mean?

A) 30
B) 29
C) 28
D) none of these

Question 24

You randomly select a sample of n = 12. What is the appropriate value for t to compute a 99% confidence interval?

A) 2.681
B) 2.718
C) 3.055
D) 3.106

Question 25

You randomly select a sample of n = 21. What is the appropriate value for t to compute a 95% confidence interval?

A) 1.721
B) 2.080
C) 2.086
D) 1.725

Question 26

You randomly draw a sample of n = 9 where $\sigma$ = 4. If the sample mean is 1, which of the following are the bounds of a 99% confidence interval?

A) -3.47, 5.47
B) -5.47, 3.47
C) -3.33, 5.33
D) -5.33, 3.33

Question 27

You randomly draw a sample of n = 12 where $\sigma$ ² = 15. If the sample mean is -25, which of the following are the bounds of a 95% confidence interval?

A) -27.44, -22.56
B) -34.43, -15.56
C) -27.46, -22.54
D) -34.53, -15.47

Question 28

You randomly select a sample of n = 30 with a mean of 6 and a standard deviation of 10.71. Determine the 95% margin of error.

A) 33%
B) 50%
C) 67%
D) 95%

Question 29

You randomly select a sample where n = 15, x̄ = 20, and s = 1.5. Determine the 95% margin of error.

A) 5.8%
B) 0.2%
C) 4.0%
D) 19.0%

Question 30

A point estimate is a single value.

Question 31

$\sigma$ is a point estimate of s.

Question 32

Point estimates provide a perfect representation of a population parameter.

Question 33

Interval estimates provide a range of values derived from a sample as an estimate of a parameter.

Question 34

A 99% interval will always be wider than a 95% interval.

Question 35

You should use a 95% confidence level because it is the most accurate level.

Question 36

If your 95% confidence interval bounds are 2 and 7, it is appropriate to conclude that there is a 95% chance that the population mean will be between 2 and 7.

Question 37

Given a 95% confidence interval, you would expect 5% of sample means to be above the interval's upper bound.

Question 38

You should use a 100% confidence level because it is the most comprehensive.

Question 39

Your population mean can change based upon the results of computing the confidence interval.

Question 40

If you are computing a 95% confidence interval when the population standard deviation is known, you should use 1.645 as your critical z.

Question 41

If you randomly select a sample of n = 16 where $\sigma$ = 4 and x̄ = 5, the boundaries of your confidence interval should be 3.04 and 6.96.

Question 42

You cannot calculate a confidence interval if you do not know the population standard deviation.

Question 43

The t-distribution was derived in order to account for the extreme scores more likely to occur in small samples.

Question 44

The shape of the t-distribution changes based upon sample size.

Question 45

When n > 10, the z-distribution and t-distribution are very similar.

Question 46

If you want to calculate a 99% confidence interval when n = 22, the value for t should 2.819.

Question 47

The margin of error generally refers to half of the confidence interval converted to a percentage of the value being estimated.

Question 48

Explain the difference between a point estimate and an interval estimate. Give an example of each. Describe when a point estimate should be calculated versus an interval estimate.

Question 49

Why is it incorrect to make the following claim? "There is a 95% chance that the population mean falls between the lower and upper bounds of this confidence interval". What is the correct claim?

Question 50

Why do you need a different formula when calculating a confidence interval for a sample with an unknown standard deviation than for a sample with a known standard deviation?

Question 51

What is the margin of error? Explain how to interpret a "10% margin of error."

Question 52

For the dataset below, the Director of HR is interested in determining if her most aggressive employees are the ones with the highest salaries. To test this, she collected weekly salary information from business records and gave an aggression survey to current employees. The test manual for the aggression survey contains normative information: worldwide, the mean score on the aggression survey is a 3.1 and the standard deviation is 1.
a) Compute a point estimate of the Salary variable above.
b) Compute an interval estimate of the Salary variable above. Report the critical z or t used.
c) Compute a point estimate of the Survey variable above.
d) Compute an interval estimate of the Survey variable above. Report the critical z or t used.