Answers: Hypothesis Testing Review



Answers: Hypothesis Testing Review

Multiple Choice

1. C: This is what happens when we reject H0

2. E: P-value is the probability that we would obtain a sample result as far (or farther away) from the mean as our sample result.

3. C: [pic]is the probability of committing a Type I error

4. D: You reject H0 when it was false! Good Job!!

5. A: This is a z-test for means. Find [pic]. No, these will not be on the test.

6. B: This is also a z-test for means. p-value = .011

7. A: Self-explanatory

8. A: Use the table or invT.

9. A: one-sided test. [pic]

10. A: one-sided test. [pic]

11. E: Yucky question. In practice, we would never look at the data first. For the sake of solving some of these problems, you may have to.

Free Response

12. We are interested in testing the claim that the average amount of money spent by all students on textbooks for the Fall 1999 semester is $325.16.

[pic], ( = average amount of money spent by all students on textbooks, Fall 1999

We are told that the sample was selected at random. However, we do not know if it is an SRS. We will assume an SRS, understand the risk to the validity and accuracy of our results. The sample size of 75 is large enough to assume Normality of the sampling distribution, according to the Central Limit Theorem. Conditions are sufficient for independence, as it is reasonable to assume that more than 750 students were available for this study.

This information, along with the fact that we do not know (, sets the stage for a 1-Sample T-Test.

[pic]

p-value = [pic]

Because p-value > ( (.1505 > .05), we do not reject H0.

We do not have sufficient evidence to conclude that the average amount of money spent by all students on textbooks for the Fall 1999 semester is different than $325.16.

13. We are interested in testing the claim that the proportion of potential voters who favor the new candidate over the incumbent has not changed.

[pic], p = proportion of potential voters who favor the new candidate over the incumbent

We are told that the sample was selected at random. However, we do not know if it is an SRS. We will assume an SRS, understand the risk to the validity and accuracy of our results. Normality conditions are satisfied because we have at least 10 successes and failures, 223 and 192, respectively. Conditions are sufficient for independence, as it is reasonable to assume that more than 6300 voters were available for this poll.

This information sets the stage for a 1-Proportion Z-Test.

[pic]

p-value = [pic]

Because p-value < ( (.0443 ( (.1527 > .05), we do not reject H0.

We do not have sufficient evidence to conclude that the average standard release potency for all cephalothin crystals is different from 910.

b) We have committed a type II error. This error could be serious if the potency of the drugs affects their ability to effectively treat symptoms.

15. We are interested in testing the claim that the percent of graduate students living on campus is no more than 10%

[pic], p = proportion of graduate students living on campus

We are told that the sample was selected at random. However, we do not know if it is an SRS. We will assume an SRS, understand the risk to the validity and accuracy of our results. Normality conditions are satisfied because we have at least 10 successes and failures, 62 and 419, respectively. Conditions are sufficient for independence, as it is reasonable to assume that more than 4810 were available for this poll.

This information sets the stage for a 1-Proportion Z-Test.

[pic]

p-value = [pic]

Because p-value < ( (.0173 ................
................

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