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 H0: μ1 = μ2.
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 H0: μ1 = μ2.
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 n1 + n1 − 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 (n1)(n2) − 1.
Answer: FALSE
Explanation: The degrees of freedom in the two sample test of means is found by n1 + n2 − 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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