8.4 Scrubs A research hospital tries a new antibiotic scrub before surgery to see whether it can lower the rate of infections of surgi- cal sites. The old rate of infection is 4%. The null hypothesis is that the proportion of infections is 0.04, p = 0.04. Give the alternative hypothesis in words and symbols. 8.16 Scrubs Refer to Exercise 8.4. Suppose a sample of 600 surgeries with the new scrub shows 18 infections. Find the value of the test statistic, z, and explain its meaning in context. The old infection rate was 4%. 8.18 St. Louis Jury Pool St. Louis County is 24% African American. Suppose you are looking at jury pools, each with 200 members, in St. Louis County. The null hypothesis is that the probability of an African American being selected into the jury pool is 24%. a. How many African Americans would you expect on a jury pool of 200 people if the null hypothesis is true? b. Suppose pool A contains 40 African American people out of 200, and pool B contains 26 African American people out of 200. Which will have a smaller p-value and why? 8.30 Women CEOs The percentage of female CEOs in 2013 in Fortune 500 companies was 4%, according to Time magazine (March 18, 2013). Suppose a student did a survey of 250 randomly selected large companies (not Fortune 500 companies), and 15 of them had women CEOs. a. About how many of the 250 should we expect to have female CEOs if the proportion of female CEOs is 4%, as it is for the Fortune 500 companies? b. Carry out the first two steps of a hypothesis test that will test whether the population proportion of women CEOs is not 0.04. 8.44 Coin Flips A test is conducted in which a coin is flipped 30 times to test whether the coin is unbiased. The null hypothesis is that the coin is fair. The alternative is that the coin is not fair. One of the accompanying figures represents the p-value after getting 16 heads out of 30 flips, and the other represents the p-value after get- ting 18 heads out of 30 flips. Which is which, and how do you know? (A) NORMAL FLOAT AUTO REAL RADIAN MP -Prop2Test P=.715 (B) NORMAL FLOAT AUTO REAL RADIAN MP 1-Prop2Test P#.2733 8.52 Which Method? A proponent of a new proposition on a ballot wants to know the population percentage of people who sup- port the bill. Suppose a poll is taken, and 580 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence interval to answer this question? Explain. If it is a hypothesis test, state the hypotheses and find the test statistic, p-value, and conclusion. Use a 5% significance level. If a confidence interval is appropriate, find the approximate 95% confidence interval. In both cases, assume that the necessary condi- tions have been met