*Statistical Techniques in Business and Economics, 17e* (Lind)

**Chapter 11 Two-Sample Tests of Hypothesis**

** **

1) If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.

Answer: FALSE

Explanation: The test is two-tailed because we did not specify which group would have the larger mean. Also, the test is two-tailed because the null hypothesis is stated as “no difference,”

or *H*0: *μ*1 = *μ*2.

Difficulty: 1 Easy

Topic: Two-Sample Tests of Hypothesis: Independent Samples

Learning Objective: 11-01 Test a hypothesis that two independent population means are equal, assuming that the population standard deviations are known and equal.

Bloom’s: Understand

AACSB: Communication

2) If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

Answer: TRUE

Explanation: The test is two-tailed because we did not specify which group would have the larger mean. Also, the test is two-tailed because the null hypothesis is stated as “no difference,”

or *H*0: *μ*1 = *μ*2.

Difficulty: 1 Easy

Topic: Two-Sample Tests of Hypothesis: Independent Samples

Learning Objective: 11-01 Test a hypothesis that two independent population means are equal, assuming that the population standard deviations are known and equal.

Bloom’s: Understand

AACSB: Communication

3) When the standard deviations are equal but unknown, a test for the differences between two population means has *n* − 1 degrees of freedom.

Answer: FALSE

Explanation: The degrees of freedom in the two sample test of means is found by *n*1 + *n*1 − 2.

Difficulty: 1 Easy

Topic: Comparing Population Means with Unknown Population Standard Deviations

Learning Objective: 11-02 Test a hypothesis that two independent population means are equal, with unknown population standard deviations.

Bloom’s: Remember

AACSB: Communication

4) If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the sample standard deviations are pooled to compute the best estimated variance.

Answer: TRUE

Explanation: We assume the sampled populations have equal but unknown standard deviations. Because of this assumption, we combine or “pool” the sample standard deviations.

Difficulty: 1 Easy

Topic: Comparing Population Means with Unknown Population Standard Deviations

Learning Objective: 11-02 Test a hypothesis that two independent population means are equal, with unknown population standard deviations.

Bloom’s: Remember

AACSB: Communication

Accessibility: Keyboard Navigation

5) If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the degrees of freedom are computed as (*n*1)(*n*2) − 1.

Answer: FALSE

Explanation: The degrees of freedom in the two sample test of means is found by *n*1 + *n*2 − 2.

Difficulty: 1 Easy

Topic: Comparing Population Means with Unknown Population Standard Deviations

Learning Objective: 11-02 Test a hypothesis that two independent population means are equal, with unknown population standard deviations.

Bloom’s: Remember

AACSB: Communication

6) A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.

Answer: FALSE

Explanation: The professor must assume the two classes are independent and use the two-sample test of means.

Difficulty: 1 Easy

Topic: Comparing Dependent and Independent Samples

Learning Objective: 11-04 Explain the difference between dependent and independent samples.

Bloom’s: Understand

AACSB: Communication

Accessibility: Keyboard Navigation

7) If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Answer: TRUE

Explanation: There are three requirements or assumptions for the test:

- The sampled populations are approximately normally distributed.
- The sampled populations are independent.
- The standard deviations of the two populations are equal.

Difficulty: 1 Easy

Topic: Comparing Dependent and Independent Samples

Learning Objective: 11-04 Explain the difference between dependent and independent samples.

Bloom’s: Remember

AACSB: Communication

Accessibility: Keyboard Navigation

8) When dependent samples are used to test for differences in the means, we compute paired differences.

Answer: TRUE

Explanation: The sample is made up of the *differences* between the values for the related pairs of data.

Difficulty: 1 Easy

Topic: Comparing Dependent and Independent Samples

Learning Objective: 11-04 Explain the difference between dependent and independent samples.

Bloom’s: Understand

AACSB: Communication

Accessibility: Keyboard Navigation

9) If two dependent samples of size 20 are used to test the difference between the means, the degrees of freedom for a *t*-statistic are 19.

Answer: TRUE

Explanation: There are *n* − 1 degrees of freedom where *n *is the common sample size.

Difficulty: 1 Easy

Topic: Two-Sample Tests of Hypothesis: Dependent Samples

Learning Objective: 11-03 Test a hypothesis about the mean population difference between paired or dependent observations.

Bloom’s: Understand

AACSB: Communication

10) When dependent samples are used to test for differences in the means, we pool the sample variances.

Answer: FALSE

Explanation: When dependent samples are used to test for differences in means, the sample variances are not pooled. We compute the variance of the differences between the paired observations.

Difficulty: 1 Easy

Topic: Two-Sample Tests of Hypothesis: Dependent Samples

Learning Objective: 11-03 Test a hypothesis about the mean population difference between paired or dependent observations.

Bloom’s: Remember

AACSB: Communication

Accessibility: Keyboard Navigation

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