Question 1

A false positive in a drug test for steroids is a Type II error.

Accepted Answer

A) True 
 B)False

Question 2

"I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is:

Accepted Answer

A) the pilot will experience the thrill of no-engine flight. 
B) the pilot will be out $1,500 unnecessarily. 
C) the mechanic will lose a good customer. 
D) impossible to determine without knowing α. 
A) the pilot will experience the thrill of no-engine flight. 
B) the pilot will be out $1,500 unnecessarily. 
C) the mechanic will lose a good customer. 
D) impossible to determine without knowing α.

Question 3

Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percentage has risen would be:

Accepted Answer

A) 2.687 
B) 2.758 
C) .0256 
D) 2.258 
A) 2.687 
B) 2.758 
C) .0256 
D) 2.258

Question 4

For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.

Accepted Answer

A) True 
 B)False

Question 5

The power of a test is the probability that the test will reject a false null hypothesis.

Accepted Answer

A) True 
 B)False

Question 6

Hypothesis tests for a mean using the critical value method require:

Accepted Answer

A) using a two-tailed test. 
B) sampling a normal population. 
C) knowing the true population mean. 
D) specifying α in advance. 
A) using a two-tailed test. 
B) sampling a normal population. 
C) knowing the true population mean. 
D) specifying α in advance.

Question 7

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of the test statistic for her hypothesis is:

Accepted Answer

A) 2.080 
B) 0.481 
C) 1.866 
D) 2.000 
A) 2.080 
B) 0.481 
C) 1.866 
D) 2.000

Question 8

The level of significance refers to the probability of making a Type II error.

Accepted Answer

A) True 
 B)False

Question 9

John rejected H0, so we know definitely that he did not commit a Type II error.

Accepted Answer

A) True 
 B)False

Question 10

In the hypothesis H0: μ = μ0, the value of μ0 is not derived from:

Accepted Answer

A) the sample. 
B) past experience. 
C) a target or benchmark. 
D) a scientific theory. 
A) the sample. 
B) past experience. 
C) a target or benchmark. 
D) a scientific theory.

Question 11

The level of significance refers to the probability of making a Type I error.

Accepted Answer

A) True 
 B)False

Question 12

In a statistical test we:

Accepted Answer

A) try to reject the null hypothesis. 
B) try to prove the alternative hypothesis. 
C) choose a null hypothesis that is easy to reject. 
D) choose a large level of significance if possible. 
A) try to reject the null hypothesis. 
B) try to prove the alternative hypothesis. 
C) choose a null hypothesis that is easy to reject. 
D) choose a large level of significance if possible.

Question 13

In a left-tailed test, a statistician got a z test statistic of -1.61. What is the p-value?

Accepted Answer

A) .4292 
B) .0709 
C) .0537 
D) .0301 
A) .4292 
B) .0709 
C) .0537 
D) .0301

Question 14

Pedro hypothesizes that more than half of his classmates would prefer a virtual web graduation ceremony, rather than sitting in the hot sun during the commencement speech. He takes a random sample of his classmates and performs a test. The results shown below are from MegaStat. What would Pedro conclude from this test? Explain carefully.
$$\begin{array} { | c c l | } 
\hline \text { Observed } & \text { Hypothesized } & \
0.6 & 0.5 & \mathrm { p } \text { (as decimal) } \
15 / 25 & 13 / 25 & \mathrm { p } \text { (as fraction) } \
15 . & 12.5 & \mathrm { X } \
25 & 25 & \mathrm { n } \
& & \
0.1 & \text { std. error } & \
1.00 & \mathrm { z } & \
.1587 & \text { p-value (one-tailed, upper) } \
\hline
\end{array}$$

Accepted Answer

The p-value says that a sample proportio

Question 15

Which is an invalid alternative hypothesis?

Accepted Answer

A) H1: μ ≠ 18 B) H1: μ = 18 C) H1: μ > 18 D) H1: μ < 18 A) H1: μ ≠ 18 B) H1: μ = 18 C) H1: μ > 18 D) H1: μ < 18

Question 16

The rejection region in a hypothesis test:

Accepted Answer

A) is an area in the tail(s) of a sampling distribution. 
B) is a consensus formed by trained statisticians. 
C) is always set to correspond to α = .05 in the test. 
D) is always equal to the p-value in the test. 
A) is an area in the tail(s) of a sampling distribution. 
B) is a consensus formed by trained statisticians. 
C) is always set to correspond to α = .05 in the test. 
D) is always equal to the p-value in the test.

Question 17

When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.

Accepted Answer

A) True 
 B)False

Question 18

For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error:

Accepted Answer

A) remains unchanged. 
B) increases. 
C) decreases. 
D) is impossible to determine without more information. 
A) remains unchanged. 
B) increases. 
C) decreases. 
D) is impossible to determine without more information.

Question 19

For tests of a mean, if other factors are held constant, which statement is correct?

Accepted Answer

A) The critical value of Student's t increases as n increases. 
B) A test statistic tcalc = 1.853 with n = 16 leads to rejection at α = .05 in a one-tailed test. 
C) It is harder to reject the null hypothesis in a two-tailed test rather than a one-tailed test. 
D) If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis. 
A) The critical value of Student's t increases as n increases. 
B) A test statistic tcalc = 1.853 with n = 16 leads to rejection at α = .05 in a one-tailed test. 
C) It is harder to reject the null hypothesis in a two-tailed test rather than a one-tailed test. 
D) If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

Question 20

A two-tailed hypothesis test for H0: π = .30 at α = .05 is analogous to:

Accepted Answer

A) asking if the 90 percent confidence interval for π contains .30. 
B) asking if the 95 percent confidence interval for π contains .30. 
C) asking if the p-value (area in both tails combined) is less than .025. 
D) asking if the p-value (area in both tails combined) is less than .10. 
A) asking if the 90 percent confidence interval for π contains .30. 
B) asking if the 95 percent confidence interval for π contains .30. 
C) asking if the p-value (area in both tails combined) is less than .025. 
D) asking if the p-value (area in both tails combined) is less than .10.

A false positive in a drug test for steroids is a Type II error.

Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percentage has risen would be:

For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.

The power of a test is the probability that the test will reject a false null hypothesis.

Hypothesis tests for a mean using the critical value method require:

The level of significance refers to the probability of making a Type II error.

John rejected H₀, so we know definitely that he did not commit a Type II error.

In the hypothesis H₀: μ = μ₀, the value of μ₀ is not derived from:

The level of significance refers to the probability of making a Type I error.

In a statistical test we:

In a left-tailed test, a statistician got a z test statistic of -1.61. What is the p-value?

Which is an invalid alternative hypothesis?

The rejection region in a hypothesis test:

When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.

For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error:

For tests of a mean, if other factors are held constant, which statement is correct?

A two-tailed hypothesis test for H₀: π = .30 at α = .05 is analogous to:

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

A false positive in a drug test for steroids is a Type II error.

Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percentage has risen would be:

For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.

The power of a test is the probability that the test will reject a false null hypothesis.

Hypothesis tests for a mean using the critical value method require:

The level of significance refers to the probability of making a Type II error.

John rejected H0, so we know definitely that he did not commit a Type II error.

In the hypothesis H0: μ = μ0, the value of μ0 is not derived from:

The level of significance refers to the probability of making a Type I error.

In a statistical test we:

In a left-tailed test, a statistician got a z test statistic of -1.61. What is the p-value?

Which is an invalid alternative hypothesis?

The rejection region in a hypothesis test:

When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.

For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error:

For tests of a mean, if other factors are held constant, which statement is correct?

A two-tailed hypothesis test for H0: π = .30 at α = .05 is analogous to:

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

John rejected H₀, so we know definitely that he did not commit a Type II error.

In the hypothesis H₀: μ = μ₀, the value of μ₀ is not derived from:

A two-tailed hypothesis test for H₀: π = .30 at α = .05 is analogous to: