The correct answer for each question is indicated by a .

1

When carrying out a sample test (with σ known) of H_{0}: µ = 10 vs. H_{a}: µ > 10 by using a rejection point, we reject H_{o} at level of significance α if and only if the calculated test statistic is:

A)

less than Z_{α}

B)

less than - Z_{α}

C)

greater than Z_{α/2}

D)

greater than Z_{α}

E)

less than the p value.

2

The manager of the quality department for a tire manufacturing company wants to study the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected.

A)

True

B)

False

3

A type I error is rejecting a true null hypothesis.

A)

True

B)

False

4

The larger the p-value, the more we doubt the null hypothesis.

A)

True

B)

False

5

A type II error is failing to reject a false null hypothesis.

A)

True

B)

False

6

For a hypothesis test about a population mean or proportion, if the level of significance is less than the p-value, the null hypothesis is rejected.

A)

True

B)

False

7

When carrying out a large sample test about a population proportion p where we are testing H_{0}: p = .4 vs. H_{a}: p < .4 and z is the calculated test statistic, we reject H_{0} at level of significance α if and only if:

A)

p < -Z_{α}

B)

Z < - Z_{α/2}

C)

Z <- Z_{α}

D)

Z > Z_{α}

8

When carrying out a sample test (with σ known) of H_{0}: µ = 10 vs. H_{α}: ≠ 10 by using a p-value, we reject H_{0} at level of significance α if and only if the p-value is:

A)

Greater than α/2.

B)

Greater than α.

C)

Less than α.

D)

Less than α/2

E)

Less than Z_{α}

9

What is the p-value when we test H_{0:} µ = 10 versus H_{a} : µ < 10 and have a calculated test statistic Z = -2.41 (σ is known)

A)

.008

B)

-.008

C)

.016

D)

.4920

E)

-.4920

10

If a null hypothesis is not rejected at a significance level of .05, it will _____ be rejected at a significance level of .01.

A)

always

B)

sometimes

C)

never

11

If we reject H_{0}:µ = 10 in favor of H_{a}:µ ≠ 10 at a given level of significance with a positive value of the test statistic z, then if we test H_{0}:µ = 10 versus H_{a}:µ > 10 using the same sample, H_{a}:µ > 10 will __________ be rejected at the same significance level.

A)

Always

B)

Sometimes

C)

Never

12

Type II error is defined as the probability of ______ H_{0}, when it should _______

A)

failing to reject, be rejected.

B)

failing to reject, not be rejected.

C)

rejecting, not be rejected.

D)

rejecting, be rejected.

13

A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average more than 22 points per game. Which of the following are the appropriate hypotheses for this problem?

A)

H_{0}: µ ≤ 21 vs. H_{α}: µ > 21

B)

H_{0}: µ ≤ 22 vs. H_{α}: µ > 22

C)

H_{0}: µ ≥ 21 vs. H_{α}: µ < 21

D)

H_{0}: µ ≥ 22 vs. H_{α}: µ < 22

14

If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided hypothesis (everything remaining the same) will always be rejected at the same significance level.

A)

True

B)

False

15

You cannot make a Type II error when the null hypothesis is rejected.

A)

True

B)

False

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