Chapter 8: Hypothesis Testing

A sample of n=16 individuals is selected from a population with μ=40 and σ=12, and a treatment is administered to the sample. After treatment, the sample mean is M=42. How does this sample compare to samples that should be obtained if the treatment has no effect?

a. It is an extreme value that would be very unlikely if the treatment has no effect

b. It is much the same as samples that would be obtained if the treatment has no effect

c. The mean is noticeably larger than would be expected if the treatment has no effect but it is not quite an extreme sample

d. There is no way to compare this sample with those that would be obtained if the treatment had no effect

b. It is much the same as samples that would be obtained if the treatment has no effect

A researcher selects a sample of n=20 from a normal population with μ=80 and σ=20, and treatment is administered to the sample. If a hypothesis test is used to evaluate the effect of the treatment, what is the null hypothesis?

a. μ=80

b. M=80

c. μ does not equal (=/) 80

d. M does not equal (=/) 80

a. μ=80

What is the correct decision in a hypothesis if the data produce a z-score that is in the critical region?

a. Reject H0

b. Fail to reject H0

c. Reject H1

d. Fail to reject H

a. Reject H0

A researcher administers a treatment to a sample of n=25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z=1.77. Assuming that the researcher is using a two-tailed test,

a. The researcher should reject the null hypothesis with α=.05 but not with α=.01.

b. The researcher should reject the null hypothesis with either α=.05 or α=.01.

c. The researcher should fail to reject H0

with either α=.05 or α=.01.

d. Cannot answer without additional information.

c. The researcher should fail to reject H0 with either α=.05 or α=.01

When does a researcher risk a Type 1 error?

a. anytime H0 is rejected

b. anytime H1 is rejected

c. anytime the decision is “fail to reject H0”

d. All of the other options are correct.

a. anytime H0 is rejected

Which of the following defines a Type 2 error?

a. rejecting a false null hypothesis

b. rejecting a true null hypothesis

c. failing to reject a false null hypothesis

d. failing to reject a true null hypothesis

c. failing to reject a false null hypothesis

What is a likely outcome for a hypothesis test if a treatment has a very small effect?

a. a Type I error

b. a Type II error

c. correctly reject the null hypothesis

d. correctly fail to reject the null hypothesis

b. a Type 2 error

A research report summarize the results of the hypothesis test by stating, “z=2.13, p<.05.” Which of the following is a correct interpretation of this report?

a. The null hypothesis was rejected and the probability of a Type I error is less than .05.

b. The null hypothesis was rejected and the probability of a Type II error is less than .05.

c. The null hypothesis was not rejected and the probability of a Type I error is less than .05.

d. The null hypothesis was not rejected and the probability of a Type II error is less than .05.

a. The null hypothesis was rejected and the probability of a Type 1 error is less than .05

Which of the following is not an assumption for the z-score hypothesis test?

a. The observations must be independent.

b. The value for μ must be the same after treatment as it was before treatment.

c. The value for σ must be the same after treatment as it was before treatment.

d. The sample must be obtained by random sampling

b. The value for μ must be the same after treatment as it was before treatment

A sample of n=16 individuals is selected from a population with μ=80 and σ=5, and a treatment is administered to the sample. If the treatment really does have an effect, then what would be the effect of increasing the standard deviation to σ=25?

a. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect exists.

b. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect does not exist.

c. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect exists.

d. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect does not exist

d. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect does not exist

A researcher is predicting that a treatment will increase scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test _____.

a. would be entirely in the right-hand tail of the distribution

b. would be entirely in the left-hand tail of the distribution

c. would be divided equally between the two tails of the distribution

d. cannot answer without knowing the value of the alpha level

a. would be entirely in the right-hand tail of the distribution

A sample is selected from a population with a mean µ=45 and a treatment is administered to the sample. If the treatment is exposed to produce a decrease in the scores, then what would be the null hypothesis for a directional hypothesis test?

a. µ ≥ 45

b. µ ≤ 45

c. M ≤ 45

d. M ≥ 45

a. µ ≥ 45

A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one-tailed hypothesis test, and the test produces z=-1.85. Based on this result, what is the correct statistical decision?

a. The researcher should reject the null hypothesis with α=.05 but not with α=.01.

b. The researcher should reject the null hypothesis with either α=.05 or α=.01.

c. The researcher should fail to reject H0 with either α=.05 or α=.01.

d. Cannot answer without additional information

c. The researcher should fail to reject H0 with either α=.05 or α=.01