# Lesson 20: Review for Exam 3 (223)

The following questions are intended to help you judge your preparation for this exam. Carefully work through the problems.
These questions are repeated on the preparation quiz for this lesson.

This is not designed to be a comprehensive review. There may be items on the exam that are not covered in this review. Similarly, there may be items in this review that are not tested on this exam. You are strongly encouraged to review the readings, homework exercises, and other activities from Units 1-3 as you prepare for the exam. In particular, you should go over the Review for Exam 1 and the Review for Exam 2. Use the to review definitions of important terms.

## 1 Review Questions

Questions 1 through 3: Decide which hypothesis test to use. Here is a list of hypothesis tests we have studied so far this semester. For each question identify the one hypothesis test that is most appropriate to the given situation. You may use a hypothesis test once, more than once, or not at all.

a. One sample z-test
b. One sample t-test
c. Paired-samples t-test
d. Two sample t-test
e. ANOVA
f. Test of one proportion

1. A survey was conducted by a group of state lotteries. A random sample of 2406 adults completed the survey. A total of 248 were classified as “heavy” players. Of these, 152 were male. You want to determine if the proportion of male “heavy” lottery players is different than the proportion of males in the population, which is 48.5%. Which hypothesis test would be most appropriate for this analysis?

2. A student project compared the effectiveness of two different combination locks. One of the locks turned clockwise first and the other lock turned counterclockwise first. They asked 25 students to participate in the study. Each student was given the combination to each lock and asked to open the locks. The time it took them to open each lock was recorded. They want to determine if one of the locks is easier to open. Which hypothesis test would be most appropriate for this analysis?

3. Weight gain during pregnancy of the mother is an important indicator of infant health. A simple random sample of pregnant women on Egypt, Kenya, and Mexico was used to determine if weight gain during pregnancy differed in these three countries. Which hypothesis test would be most appropriate for this analysis?

Questions 4 and 5: Decide which confidence interval to use. Here is a list of confidence intervals we have studied so far this semester. For each question identify the one confidence interval that is most appropriate for the given situation. You may use a confidence interval once, more than once, or not at all.

a. One sample z-confidence interval
b. One sample t-confidence interval
c. Paired-samples t-confidence interval
d. Two sample t-confidence interval

4. A bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure this is the case, the bank evaluates six properties that both appraisers have recently valued. Which confidence interval would be most appropriate for this study?

5. DoubleStuf Oreo cookies are supposed to have twice the filling of regular Oreo cookies. You and some friends decide you want to know if that is a true assertion by the company who makes them. You take a sample of 55 DoubleStuf Oreo cookies and measure the amount of filling in each one. You need to construct a confidence interval to estimate the true mean filling amount of DoubleStuf Oreos in order to compare it to the filling amount found in regular Oreos. Which confidence interval would be most appropriate for this study?

6. Which one of the following best defines the notion of the significance level of a hypothesis test?

a. The probability of rejecting $H_0$, whether it's true or not
b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
c. The probability of the type I error
d. The probability of the type II error

7. Which one of the following best defines the notion of the $P$-value of a hypothesis test?

a. The probability of rejecting $H_0$, whether it's true or not
b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
c. The probability of the type I error
d. The probability of the type II error

8. Suppose you create a 95% confidence interval for a mean, and get (10, 20). You've been told to report this by saying something similar to, “We are 95% confident that the true mean is between 10 and 20." Exactly what does this mean?

a. 95% of the data are between 10 and 20.
b. 95% of the sample means are between 10 and 20.
c. There is a 95% chance that the true mean is between 10 and 20.
d. 95% of all 95% confidence intervals actually contain the true mean.

Questions 9 through 11: Use the following information. You take a simple random sample of 100 adults from a town in the Western United States to determine the proportion of adults in the town who invest in the stock market. Assume the unknown population proportion or percentage of people in town who invest in the stock market is $p=0.30$ (or 30%).

9. What is the mean of the distribution of the sample proportions?

a. 30
b. 70
c. 0.70
d. 0.30

10. What is the standard deviation of the distribution of the sample proportions?

a. 0.004
b. 0.046
c. 0.458
d. 4.583

11. What is the probability that your random sample of 100 adults will have a sample proportion less that 0.25?

a. 0.138
b. 0.124
c. 0.876
d. 0.862

Questions 12 through 16: Use the following information to answer each question. A recent book noted that only 20% of all investment managers outperform the Dow Jones Industrial Average over a five-year period. A random sample of 200 investment managers that had graduated from one of the top ten business programs in the country were followed over a five-year period. Fifty of these outperformed the Dow Jones Industrial Average. Let $p$ be the true proportion of investment managers who graduated from one of the top ten business programs who outperformed the Dow Jones over a five-year period.

Suppose you wish to see if there is evidence that graduates of one of the top ten business programs performs better than other investment managers. Conduct a hypothesis test. Use a level of significance of $\alpha=0.05$.

12. Which of the following pairs of hypotheses is the most appropriate for addressing this question?

a. $H_0:~p=0.2$  $H_a:~p<0.2$
b. $H_0:~p=0.2$  $H_a:~p\ne0.2$
c. $H_0:~p=0.2$  $H_a:~p>0.2$
d. $H_0:~p<0.2$  $H_a:~p=0.2$
e. $H_0:~p\ne0.2$  $H_a:~p=0.2$
f. $H_0:~p>0.2$  $H_a:~p=0.2$

13. How many measurements must you have in order to assure that $\hat p$ is normally distributed?

a. $n\ge30$
b. $n\ge5$
c. $np\ge10$ and $n(1-p)\ge10$
d. $np\ge5$ and $n(1-p)\ge5$

14. The value of your test statistic is:

a. 1.786
b. 0.039
c. 1.923
d. 0.077

15. The $P$-value of your test is:

a. 1.786
b. 0.039
c. 1.923
d. 0.077

16. Is there sufficient evidence to conclude that graduates from the top ten business programs perform better than other investment managers?

a. Yes. I rejected $H_0$.
b. Yes. I failed to reject $H_0$.
c. Yes. I accepted $H_a$.
d. No. I rejected $H_0$.
e. No. I failed to reject $H_0$.
f. No. I failed to accept $H_a$.

## 2 Lesson Outcomes

By the end of this lesson, you Should be able to:

• Identify the appropriate confidence interval to apply in a situation with categorical data
• Identify the appropriate hypothesis test to apply in a situation with categorical data
• Review what you have learned and have done in the course up to this point
• Successfully complete exam 3