1. Your sister, a consumer food advocate, is concerned about the mean fat content of the burgers you typically eat for lunch. She purchases 12 burgers from the restaurant and submits it to an independent laboratory for analysis. The percentage of fat in each burger is given by the following data: 21 18 19 16 18 24 22 19 24 14 18 15 The owner of the restaurant claims that the mean fat content of its burgers is no more than 20%. Assume that the percentage fat in a burger is normally distributed with a standard deviation of 3. Test whether there is evidence for the manufacturer's claim. Let o = 0.05 a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. C. Construct the test statistic. d. Conduct the test. e. What do you conclude? 2. Redo the previous question assuming that a is unknown. a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. e. What do you conclude?3. Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surveyed was: "Should the federal tax on cigarettes be raised to pay for health care reform?" The results of the survey were: Smokers Nonsmokers n = 195 n = 605 # said yes: 41 # said yes: 351 Test whether the groups significantly differ at the 2 percent level in their support for the excise taxes. a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. Calculate the p-value. What do you conclude?The hourly fry output by Burger Prince's fry machine is advertised to be 130 pounds. Testing a new machine for the drive-in for 22 different one-hour periods, the average production was 143 pounds, with a standard deviation of 17 pounds. At a 5% level of significance, should Burger Prince management complain? Write down the type of test Write down the null and alternative hypotheses Construct the test statistic Conduct the test. What do you conclude? AR ER Consider this interesting situation. Whole Foods has just installed Casemarc optical scanning equipment at the checkout counters of its Westside store. After one month of experimentation, management notes that the system gives a checkout rate of 6.45 items per minute. This is computed as the number of line items processed per minute of time that a checkout counter is open, and necessarily involves time for bagging groceries and processing coupons. The manager of the Westside store asked to try KingDom, an alternate system. Over the next few days, using different clerks, KingDom was evaluated for 50 separate one-hour periods. These 50 periods showed an average checkout rate of 6.61 items per minute, with a standard deviation of 0,62, Is KingDom better? Let alpha = .05. Write down the type of test you will conduct. Write down the null and alternative hypotheses. Construct the test statistic. Conduct the test. What do you conclude? LIS et T 6. A random sample of 17 police officers in Oak Park has a mean annual income of $35,800 and a standard deviation of $7,800. In Homewood, a random sample of 18 police officers has a mean annual income of $35,100 and a standard deviation of $7,375. Test the claim at o =0.01 that the mean annual incomes in the two cities are not the same. Assume the population variances are equal. a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. e. What do you conclude? 7. An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set a = .05, test to see a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test e. What do you conclude?8. Suppose the mean salary for assistant finance professors in the United States is believed to be $131,600. A sample of 25 professors revealed a mean salary of $142,400 . Assuming the standard deviation is $10,000, can it be concluded that the average salary has increased using a 0.02 level of significance? a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. e. What do you conclude? 9. Historically, evening long-distance calls from a Los Angeles have averaged 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes. Assume the standard deviation is known to be 5 minutes. Using a 0.05 level of significance, is there sufficient evidence to conclude that the average evening long-distance call has decreased? a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. e. What do you conclude?10. A high school math teacher claims that students in her class will score higher on the math portion of the ACT then students in a colleague's math class. The mean ACT math score for 49 students in her class is 22.1 and the standard deviation is 4.8. The mean ACT math score for 44 of the colleague's students is 19.8 and the standard deviation is 5.4. At o= 0.05, can the teacher's claim be supported? a. Write down the type of test you will conduct. b. Write down the null and alternative hypotheses. c. Construct the test statistic. d. Conduct the test. What do you conclude