Question 1

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except​

Accepted Answer

A)  ​use the sample proportion from a previous study. 
B)  ​use the sample proportion from a preliminary sample. 
C)  ​use 1.0 as an estimate. 
D)  ​use judgment or a best guess. 
A)  ​use the sample proportion from a previous study. 
B)  ​use the sample proportion from a preliminary sample. 
C)  ​use 1.0 as an estimate. 
D)  ​use judgment or a best guess.

Question 2

A random sample of 25,000 ACT test takers had an average score of 21 with a standard deviation of 5. What is the 95% confidence interval of the population mean?

Accepted Answer

A)  4.9723 to 5.0277 
B)  4.9380 to 5.0620 
C)  4.7397 to 5.2603 
D)  4.9432 to 5.0568 
A)  4.9723 to 5.0277 
B)  4.9380 to 5.0620 
C)  4.7397 to 5.2603 
D)  4.9432 to 5.0568

Question 3

In interval estimation, as the sample size becomes larger, the interval estimate

Accepted Answer

A)  becomes narrower. 
B)  becomes wider. 
C)  remains the same, because the mean is not changing. 
D)  gets closer to 1.96. 
A)  becomes narrower. 
B)  becomes wider. 
C)  remains the same, because the mean is not changing. 
D)  gets closer to 1.96.

Question 4

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).

Accepted Answer

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. 
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.

Question 5

The use of the normal probability distribution as an approximation of the sampling distribution of   is based on the condition that both np and n(1 - p) equal or exceed​

Accepted Answer

A)  ​.05. 
B)  ​5. 
C)  ​10. 
D)  ​30. 
A)  ​.05. 
B)  ​5. 
C)  ​10. 
D)  ​30.

Question 6

A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ

Accepted Answer

A)  becomes narrower. 
B)  becomes wider. 
C)  does not change. 
D)  becomes 100.1 to 120.1. 
A)  becomes narrower. 
B)  becomes wider. 
C)  does not change. 
D)  becomes 100.1 to 120.1.

Question 7

The z value for a 97.8% confidence interval estimation is

Accepted Answer

A)  2.02. 
B)  1.96. 
C)  2.00. 
D)  2.29. 
A)  2.02. 
B)  1.96. 
C)  2.00. 
D)  2.29.

Question 8

When the level of confidence decreases, the margin of error

Accepted Answer

A)  stays the same. 
B)  becomes smaller. 
C)  becomes larger. 
D)  becomes smaller or larger, depending on the sample mean. 
A)  stays the same. 
B)  becomes smaller. 
C)  becomes larger. 
D)  becomes smaller or larger, depending on the sample mean.

Question 9

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

Accepted Answer

A)  83.45 to 84.55. 
B)  80.07 to 87.93. 
C)  83.29 to 84.71. 
D)  80.5 to 87.5. 
A)  83.45 to 84.55. 
B)  80.07 to 87.93. 
C)  83.29 to 84.71. 
D)  80.5 to 87.5.

Question 10

The degrees of freedom associated with a t distribution are a function of the​

Accepted Answer

A)  ​area in the upper tail. 
B)  ​sample standard deviation. 
C)  ​confidence coefficient. 
D)  ​sample size. 
A)  ​area in the upper tail. 
B)  ​sample standard deviation. 
C)  ​confidence coefficient. 
D)  ​sample size.

Question 11

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

Accepted Answer

A)  uniform 
B)  normal 
C)  exponential 
D)  p 
A)  uniform 
B)  normal 
C)  exponential 
D)  p

Question 12

In a random sample of 100 observations,   = .2. The 95% confidence interval for p is

Accepted Answer

A)  .1342 to .2658. 
B)  .15 to .25. 
C)  0 to .4. 
D)  .1216 to .2784. 
A)  .1342 to .2658. 
B)  .15 to .25. 
C)  0 to .4. 
D)  .1216 to .2784.

Question 13

From a population with a variance of 484, a sample of 256 items is selected. At 95% confidence, the margin of error is

Accepted Answer

A)  16. 
B)  1.375. 
C)  2.695. 
D)  22. 
A)  16. 
B)  1.375. 
C)  2.695. 
D)  22.

Question 14

As the sample size increases, the margin of error

Accepted Answer

A)  increases. 
B)  decreases. 
C)  stays the same. 
D)  fluctuates depending on the mean. 
A)  increases. 
B)  decreases. 
C)  stays the same. 
D)  fluctuates depending on the mean.

Question 15

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when​

Accepted Answer

A)  ​np > 5. 
B)  ​n(1 - p) > 5. 
C)  ​p has a normal distribution. 
D)  ​both np > 5 and n(1 - p) > 5. 
A)  ​np > 5. 
B)  ​n(1 - p) > 5. 
C)  ​p has a normal distribution. 
D)  ​both np > 5 and n(1 - p) > 5.

Question 16

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 64 business students over a one-week period. Assume the population standard deviation is 1.6 hours. If the sample mean is 9 hours, then the 95% confidence interval is _____ hours.

Accepted Answer

A)  7.04 to 10.96 
B)  7.36 to 10.64 
C)  7.80 to 10.20 
D)  8.608 to 9.392 
A)  7.04 to 10.96 
B)  7.36 to 10.64 
C)  7.80 to 10.20 
D)  8.608 to 9.392

Question 17

In general, higher confidence levels provide

Accepted Answer

A)  wider confidence intervals. 
B)  narrower confidence intervals. 
C)  a smaller standard error. 
D)  unbiased estimates. 
A)  wider confidence intervals. 
B)  narrower confidence intervals. 
C)  a smaller standard error. 
D)  unbiased estimates.

Question 18

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

Accepted Answer

A)  ​varies from sample to sample of the same size. 
B)  ​is the same for all samples of the same size. 
C)  ​increases as the sample size increases. 
D)  ​is independent of sample size. 
A)  ​varies from sample to sample of the same size. 
B)  ​is the same for all samples of the same size. 
C)  ​increases as the sample size increases. 
D)  ​is independent of sample size.

Question 19

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

Accepted Answer

A)  becomes larger. 
B)  becomes smaller. 
C)  stays the same. 
D)  fluctuates. 
A)  becomes larger. 
B)  becomes smaller. 
C)  stays the same. 
D)  fluctuates.

Question 20

A population has a standard deviation of 25. A random sample of 125 items from this population is selected. The sample mean is determined to be 325. At 95% confidence, the margin of error is

Accepted Answer

A)  2.24. 
B)  5. 
C)  4.38. 
D)  11.18. 
A)  2.24. 
B)  5. 
C)  4.38. 
D)  11.18.

Exam 8: Interval Estimation

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except​

A random sample of 25,000 ACT test takers had an average score of 21 with a standard deviation of 5. What is the 95% confidence interval of the population mean?

In interval estimation, as the sample size becomes larger, the interval estimate

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).

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed​

A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ

The z value for a 97.8% confidence interval estimation is

When the level of confidence decreases, the margin of error

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

The degrees of freedom associated with a t distribution are a function of the​

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

In a random sample of 100 observations, = .2. The 95% confidence interval for p is

From a population with a variance of 484, a sample of 256 items is selected. At 95% confidence, the margin of error is

As the sample size increases, the margin of error

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when​

In general, higher confidence levels provide

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A population has a standard deviation of 25. A random sample of 125 items from this population is selected. The sample mean is determined to be 325. At 95% confidence, the margin of error is

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To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed

The degrees of freedom associated with a t distribution are a function of the

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when