Homework 20 AP Statistics Spring 2017 1. A psychologist claims that the mean age at which children start walking is 12.5 months. The following data give the age at which 18 randomly selected children started walking. 15 11 13 14 15 12 15 10 16 17 14 16 13 15 15 14 11 13 Test at the 1% level of significance if the mean age at which children start walking is different from 12.5 months. 2. In each of the following situations, is the alternative hypothesis one-sided or twosided? What are the hypotheses? a. A business student conducts a taste test to see whether students prefer Diet Coke or Diet Pepsi. b. PepsiCo recently reformulated Diet Pepsi in an attempt to appeal to teenagers. They run a taste test to see if the new formula appeals to more teenagers than the standard formula. c. A budget override in a small town requires a two-thirds majority to pass. A local newspaper conducts a poll to see if there’s evidence it will pass. d. One financial theory states that the stock market will go up or down with equal probability. A student collects data over several years to test the theory. 3. A sample of 800 items produced on a new machine showed that 48 of them are defective. The factory will get rid of the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not? 4. According to official census figures, 8% of couples living together are not married. A researcher took a random sample of 400 couples and found that 9.5% of them are not married. Test the 15% significance level if the current percentage of unmarried couples is different from 8%. 5. In a survey of 1273 adults, 52% said it is not morally wrong to change the genetic makeup of human cells. What test would be indicated to address the following statement: “The majority of adults do not think it is morally wrong to change the genetic makeup of human cells”? Note: “majority” means “greater than 50%”. 6. Conduct the test from number 5. 7. Soon after the Euro was introduced as currency in Europe, it was widely reported that some-one had spun a Euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin. a. Estimate the true proportion of heads. Use a 95% confidence interval. Don’t forget to check the conditions. b. Does your confidence interval provide evidence that the coin is unfair when spun? Explain. c. What is the significance level of this test? Explain. 8. A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet standards. a. In this context, what is a Type I error? b. In this context, what is a Type II error? c. Which type of error would the shop’s owner consider more serious? d. Which type of error might environmentalists consider more serious? 9. Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention. a. State appropriate null and alternative hypotheses in this setting. Be sure to define your parameters. b. Describe a Type I and a Type II error, and explain the consequences of each. c. The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller. Explain. 10. A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company’s hiring practices are discriminatory? a. Is this a one-tailed or a two-tailed test? Why? b. In this context, what would a Type I error be? c. In this context, what would a Type II error be? d. In this context, what is meant by the power of the test? e. If the hypothesis is tested at the 5% level of significance instead of 1%, how will this affect the power of the test? f. The lawsuit is based on the hiring of 37 employees. Is the power of the test higher than, lower than, or the same as it would be if it were based on 87 hires?