# Statistics in a Modern World 800 Homework 8 NAME:_________________________________

Homework 8 Exercises Assigned from Chapters 22-23 (26 pts.) due Fri. Nov. 20 in Lecture.

### CHAPTER 22

#11 (2 pts.) Given the convention of declaring that a result is statistically significant if the p-value is 0.05 or less, what decision would be made in each case?

1. p-value = 0.35 (i) reject the null hypothesis (ii) do not reject the null hypothesis
2. p-value = 0.04 (i) reject the null hypothesis (ii) do not reject the null hypothesis

#12a (1 pt.) In previous chapters, we learned that researchers have discovered a link between vertex baldness and heart attacks in men. State the null and alternative hypotheses used to investigate whether there is such a relationship.

#14 (3 pts.) Suppose that a study is designed to choose between the hypotheses:

Null hypothesis: Population proportion is 0.25

Alternative hypothesis: Population proportion is higher than 0.25

On the basis of a sample of size 500, the sample proportion is 0.29. The standard deviation for the potential sample proportions in this case is about 0.02.

1. Compute the z statistic corresponding to the sample proportion of 0.29, assuming the null hypothesis is true.
2.

3. What is the p-value?
4. Based on the results of parts (a) and (b), make a conclusion: (i) population proportion may be 0.25 (ii) population proportion is higher than 0.25

### CHAPTER 23

#1 (3 pts.) In Exercise 12 in Chapter 20, we learned that in a survey of 507 adult American Catholics, 59% answered yes to the question, "Do you favor allowing women to be priests?"

1. Set up the null and alternative hypotheses for deciding whether a majority of American Catholics favor allowing women to be priests.
2.

3. Using Example 3 p.437 as a guide, compute the test statistic for this situation.
4.

5. If you have done everything correctly, the p-value for the test is about 0.00005. Based on this, make a conclusion for this situation: (i) A majority of American Catholics favor allowing women to be priests (ii) A majority of American Catholics do not necessarily favor allowing women to be priests

#3 (1 pt.) Suppose a one-sided test for a proportion resulted in a p-value of 0.03. What would the p-value be if the test were two-sided instead?

#5 (1 pt.) Suppose you were given a hypothesized population mean, a sample mean, a sample standard deviation, and a sample size for a study involving a random sample from one population. What would you use as the test statistic? (i) z (ii) t (iii) chi-square

#6 (3 pts.) For each z statistic, use normal tables (p.157) to find the p-value for each of these examples taking into account whether the test is one-sided or two-sided:

1. Chapter 23, Example 2, z=2.17, two-sided test
2. Chapter 22, Example 1, z=2.00, one-sided test
3. Case Study 22.1, z=4.09, one-sided test

#9 (2 pts.) On July 1, 1994, The Press of Atlantic City, NJ, had a headline reading, "Study: Female hormone makes mind keener"; (p. A2) Here is part of the report:

"Halbreich said he tested 36 post-menopausal women before and after they started the estrogen therapy. He gave each one a battery of tests that measured such things as memory, hand-eye coordination, reflexes and the ability to learn new information and apply it to a problem. After estrogen therapy started, he said, there was a subtle but statistically significant increase in the mental scores of the patients."

1. State the appropriate null and alternative hypotheses.
2.

3. What type of study is this? (i) matched pairs (ii) two-sample

### CHAPTER 23

#12 (3 pts.) Example 2 in this Chapter tested whether the average fat lost from 1 year of dieting versus 1 year of exercise could be equivalent. The study also measured lean body weight (muscle) lost or gained

1. If muscle weight change is compared for men who diet only and men who exercise only, would we have reason to set up a one-sided or two-sided test?
2. The p-value for the one-sided test is .004. What would it have been for a two-sided test?
3. Is there evidence that men who exercise only don't lose as much muscle weight? Answer yes or no.

#14 (7 pts.) On January 30, 1995, Time magazine reported the results of a poll of adult Americans, in which they were asked, "Have you ever driven a car when you probably had too much alcohol to drive safely?" The exact results were not given, but from the information provided we can guess at what they were. Of the 300 men who answered, 189 (63%) said yes and 108 (36%) said no. The remaining 3 weren't sure. Of the 300 women, 87 (29%) said yes while 210 (70%) said no, and the remaining 3 weren't sure.

1. Organize the data into a two-by-two table, ignoring the "not sure" answers.
2. State the appropriate null and alternative hypotheses.
3. Set up a table of numbers expected if the null hypothesis were true.
4. Set up a table comparing the observed and expected numbers, as on pp. 250-251.
5. Calculate the chi-squared statistic.
6. The p-value is (i) more than .05 (ii) less than .05.
7. State your conclusion: there (i) IS (ii) IS NOT NECESSARILY a relationship between gender and response to the question.

### CHAPTER 24 Problems should be done for practice but not handed in!

#2a Refer to Case Study 24.2 p.459, in which a report stated that Internet use was associated with a statistically significant increase in drpression. Which type of hypothesis test would have been more appropriate? (i) one-sided (ii) two-sided

#17 Would it be easier to reject hypotheses about populations that had a lot of natural variability in the measurements or a little variability in the measurements?

(i) a lot (ii) a little