Directions: Give the null and the alternative hypotheses for the following situations. You only need to set up the hypotheses in this part. Make sure to use the appropriate parameter symbol in the statement of the hypotheses: p or u. The null and alternative hypothesis has been given for the rst problem. 1. The average number of daily accidents at a particular mine since the year 2000 has been 7.6. In an effort to reduce this number, management instituted a massive safety program in June 2012. To determine the effectiveness of the program, a random sample of 45 days will be taken. Is there evidence that daily accidents have decreased since the institution of the new program? 2. A women's group has claimed that female employees are passed over for management training at a large supermarket chain. The company denies this claim saying they select employees at random from an eligible pool of 1000 employees. The women's group has hired a statistician to evaluate the data from the management training program to see if it supports their claim. The eligible pool was 40% female and 60% male. 3. Welfare department ofcials of a certain city claim that the average number of cases of child abuse handled daily by its various agencies is 7.62. A newspaper reporter decides to test this claim. The reporter will select 40 days and determine the average number of cases handled on these days. Using a 10% level of significance, should we reject the welfare department ofcials' claim? 4. Industry representatives claim that the average price of an introductory math textbook is $93.50. Numerous student groups claim that the average price is considerably higher. A survey of 9 such books will be taken, using a 5% level of signicance, should we reject the industry representative's claim in favor of the student groups' claim? 5. A large express-delivery service has had a history of misrouting approximately 4.2% of the packages each day. During a trial period of a new sorting system, a random sample of 400 packages will be tracked. Is there sufficient evidence that the new sorting system works better than the old one and should be implemented on a permanent basis? 6. In an effort to attract new industry to the region, a mayor claims that the average age of a worker in the region is 27 years with a standard deviation of 5.72 years. A prospective company is interested in determining whether the mayor's claim is accurate. A random sample of 60 workers will be checked. Is there evidence to conclude that the average age is not 27? Use or = .05. Ho: Ha: Ho: Ha: Ho: Ha: Ho: Ha: Ho: Ha: Ho: Ha: u$93.50 [31:92 pl>p2 11:2 7 \"$27 2. Refer to Problem 5 in PART I. If you were in charge of the sorting center, would you want a reasonable amount of evidence or very strong evidence that the new sorting system worked better before implementing it on a permanent basis? Explain your response. Either answer may be acceptable, but explain your choice! Based on the amount of evidence you just said you would like, should you use a significance level of .01 or a significance level of . 10? Explain your reasoning. 3. Refer to Problem 8 in PART I. Suppose that after running the test, the P-value was .063. What statement should the Consumer Fraud Bureau make about whether or not the customers were being short-changed? Complete the statement below and then explain the statistical support for your statement. "After investigating a sample of jars of coffee, we found that ... 4. Select one of the Problems in PART I and CLEARLY explain, using the CONTEXT of the situation the difference between making a Type I Error and making a Type II Error. I chose problem Type I: Type II: In this situation, which type of error has the more serious consequences, and for whom? Explain your choices.7. A group of urologists claim that the average length of a hospital stay for a patient with Ho: 1=9.2 one type of kidney disease is 9.2 days. An insurance company examinees a random sample of 36 patients recently treated for this ailment. Should the insurance company base its projected Ha: 149.2 Reimbursement costs on an average of 9.2 days? 8. A coffee manufacturer sells jars of coffee supposedly filled with 10 ounces of coffee. The Consumer Fraud Bureau of a state has received numerous complaints that some of the jars Ho: u=10 contain less than the specified 10 ounces. The Bureau decides to investigate these complaints by sampling 100 jars. Does the data indicate that the coffee manufacturer can be accused of Ha: p2 in election? PART II: UNDERSTANDING TYPES OF ERRORS 1. Refer to Problem 2 in PART I. Stating the hypotheses in words, rather than in terms of the population proportion would yield: Ho: The supermarket chain is fair to women seeking management positions. Ha: The supermarket chain is NOT fair to women seeking management positions. Explain the consequences of making a Type I error in this situation. (Hint: Decide what the result of the test is. If there's an error, then that result of the test is actually not true. So, an error has been made. So, what are the consequences of making that mistake?)