Question 1

The power of a test is the probability of:

Accepted Answer

A) concluding H1 when H1 is true. 
B) concluding H1 when H0 is true. 
C) concluding H0 when H0 is true. 
D) concluding H0 when H1 is true. 
A) concluding H1 when H1 is true. 
B) concluding H1 when H0 is true. 
C) concluding H0 when H0 is true. 
D) concluding H0 when H1 is true.

Question 2

Varying the true mean is a movement along the power curve, not a shift in the curve.

Accepted Answer

A) True 
 B)False

Question 3

High power in a hypothesis test about one sample mean is likely to be associated with:

Accepted Answer

A) small sample size. 
B) low α. 
C) large β. 
D) small σ. 
A) small sample size. 
B) low α. 
C) large β. 
D) small σ.

Question 4

If the hypothesized proportion is π0 = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.

Accepted Answer

A) True 
 B)False

Question 5

A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.

Accepted Answer

A) True 
 B)False

Question 6

Which of the following statements is true?

Accepted Answer

A) Decreasing α will increase the power of the test. 
B) Doubling the sample size will double the power of the test. 
C) A higher standard deviation would increase the power if we are testing a mean. 
D) Power of the test rises if the true mean is farther from the hypothesized mean. 
A) Decreasing α will increase the power of the test. 
B) Doubling the sample size will double the power of the test. 
C) A higher standard deviation would increase the power if we are testing a mean. 
D) Power of the test rises if the true mean is farther from the hypothesized mean.

Question 7

The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.

Accepted Answer

A) True 
 B)False

Question 8

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at α = .05, which is the most accurate statement?

Accepted Answer

A) We would strongly reject the claim. 
B) We would clearly fail to reject the claim. 
C) We would face a rather close decision. 
D) We would switch to α = .01 for a more powerful test. 
A) We would strongly reject the claim. 
B) We would clearly fail to reject the claim. 
C) We would face a rather close decision. 
D) We would switch to α = .01 for a more powerful test.

Question 9

For a sample size of n = 100, and σ = 10, we want to test the hypothesis H0: μ = 100. The sample mean is 103. The test statistic is:

Accepted Answer

A) 1.645 
B) 1.960 
C) 3.000 
D) 0.300 
A) 1.645 
B) 1.960 
C) 3.000 
D) 0.300

Question 10

To test the hypothesis H0: π = .0125 using n = 160, it is safe to assume normality of p.

Accepted Answer

A) True 
 B)False

Question 11

Bob hypothesizes that the average student at his university has to take more than 130 credits to graduate. He takes a random sample of his classmates and performs a test. The results shown below are from MegaStat. What would Bob conclude from this test? Explain carefully.
Hypothesis Test: Mean vs. Hypothesized Value
$130.000$ $ \quad $hypothesized value
$134.500$ $ \quad $mean Credits
$10.029$ $ \quad $std. dev.
$1.967$ $ \quad $std. error
$\begin{array} { l l } 26 & \text { n } \ 25 & \text { df } \end{array}$
$2.29 $$ \quad $t
$.0154 $$ \quad $p-value (one-tailed, upper)

Accepted Answer

The p-value says that a sample mean such

Question 12

John rejected his null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

Accepted Answer

A) John did not commit a Type I error. 
B) John did not commit a Type II error. 
C) John committed neither a Type I nor Type II error. 
D) John committed both a Type I and a Type II error. 
A) John did not commit a Type I error. 
B) John did not commit a Type II error. 
C) John committed neither a Type I nor Type II error. 
D) John committed both a Type I and a Type II error.

Question 13

Which of the following is not a characteristic of the t distribution?

Accepted Answer

A) It is a continuous distribution. 
B) It has a mean of zero. 
C) It a symmetric distribution. 
D) It is similar to the z distribution when n is small. 
A) It is a continuous distribution. 
B) It has a mean of zero. 
C) It a symmetric distribution. 
D) It is similar to the z distribution when n is small.

Question 14

Why is it better to say "fail to reject H0" instead of "accept H0"?

Accepted Answer

A different sample could lead

Question 15

When σ is unknown, it is more conservative to use z instead of t for the critical value.

Accepted Answer

A) True 
 B)False

Question 16

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. In this problem:

Accepted Answer

A) normality of the sample proportion should not be assumed. 
B) normality of the sample proportion can be assumed. 
C) normality of the sample proportion cannot be judged without knowing π. 
A) normality of the sample proportion should not be assumed. 
B) normality of the sample proportion can be assumed. 
C) normality of the sample proportion cannot be judged without knowing π.

Question 17

The power curve plots β on the Y-axis and the test statistic on the X-axis.

Accepted Answer

A) True 
 B)False

Question 18

If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

Accepted Answer

A) True 
 B)False

Question 19

In hypothesis testing, the value of β is:

Accepted Answer

A) equal to 1 minus the probability of committing a Type I error. 
B) the probability of concluding H0 when H0 is true. 
C) the probability of concluding H0 when H1 is true. 
A) equal to 1 minus the probability of committing a Type I error. 
B) the probability of concluding H0 when H0 is true. 
C) the probability of concluding H0 when H1 is true.

Question 20

The probability of a false positive is decreased if we reduce α.

Accepted Answer

A) True 
 B)False

The power of a test is the probability of:

Varying the true mean is a movement along the power curve, not a shift in the curve.

High power in a hypothesis test about one sample mean is likely to be associated with:

If the hypothesized proportion is π₀ = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.

A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.

Which of the following statements is true?

The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.

For a sample size of n = 100, and σ = 10, we want to test the hypothesis H₀: μ = 100. The sample mean is 103. The test statistic is:

To test the hypothesis H₀: π = .0125 using n = 160, it is safe to assume normality of p.

John rejected his null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

Which of the following is not a characteristic of the t distribution?

Why is it better to say "fail to reject H₀" instead of "accept H₀"?

When σ is unknown, it is more conservative to use z instead of t for the critical value.

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. In this problem:

The power curve plots β on the Y-axis and the test statistic on the X-axis.

If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

In hypothesis testing, the value of β is:

The probability of a false positive is decreased if we reduce α.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 9: One-Sample Hypothesis Tests

The power of a test is the probability of:

Varying the true mean is a movement along the power curve, not a shift in the curve.

High power in a hypothesis test about one sample mean is likely to be associated with:

If the hypothesized proportion is π0 = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.

A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.

Which of the following statements is true?

The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.

For a sample size of n = 100, and σ = 10, we want to test the hypothesis H0: μ = 100. The sample mean is 103. The test statistic is:

To test the hypothesis H0: π = .0125 using n = 160, it is safe to assume normality of p.

John rejected his null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

Which of the following is not a characteristic of the t distribution?

Why is it better to say "fail to reject H0" instead of "accept H0"?

When σ is unknown, it is more conservative to use z instead of t for the critical value.

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. In this problem:

The power curve plots β on the Y-axis and the test statistic on the X-axis.

If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

In hypothesis testing, the value of β is:

The probability of a false positive is decreased if we reduce α.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

If the hypothesized proportion is π₀ = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.

For a sample size of n = 100, and σ = 10, we want to test the hypothesis H₀: μ = 100. The sample mean is 103. The test statistic is:

To test the hypothesis H₀: π = .0125 using n = 160, it is safe to assume normality of p.

Why is it better to say "fail to reject H₀" instead of "accept H₀"?