Only the questions on the last image. (Part III)

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 '16. In an effort to reduce this number, management instituted a massive safety program in June 2012. To determine the e'ectiveness 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 signicance, 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 indusz 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 sufcient 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 2?? Use or. = .05. 7. A group of urologists claim that the average length of a hospital stay for a patient with 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 Reimbursement costs on an average of 9.2 days? 8. A coffee manufacturer sells jars of coffee supposedly lled with 10 ounces of coffee. The Consumer Fraud Bureau of a state has received numerous complaints that some of the jars contain less than the specied 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 "short-changing" the customer? Use a 5% level of signicance. 9. In an ABC! Washington Post survey 855 randomly selected Americans listed gun control as an important issue in elections. Can ABC and the Washingmn Post claim that this survey provides sufcient evidence to say that a majority of Americans consider gun control an important issue in election? Ho: Ho Ho: Ho: Ho: Ho: Ho: Ho: Ho: jI.=?.6 up2 P=27 p=9.2 #9.: p=1ll pp2 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?) When super market chain is fair to women, we conclude that it is not fair for women seeking management positions. The consequences will be that we will unnecessarily bring honest companies into the allegation of the wrongdoing. 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! You would want very strong evidence because unless the new system has a significant upside, it would not be smart to bring about a large setup cost for the new system when it can only bring a small upside in the accuracy. 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. Since I want very strong evidence, I would choose 0.01. Because of the smaller rejection in comparison to 0.1. 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 the customers were not being short-changed." P - value = 0.063 > 0.05 = sig. level, failure to reject null. 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 8. Type I: When customers are not being short-changed, and CFB concludes that they are. Type II: When customers truly are being short-changed, but CFB says that they are not. In this situation, which type of error has the more serious consequences, and for whom? Explain your choices. Type II error has more serious consequences for customers because although they are actually getting cheated, they will not get justice.Part III: Practicing Carrying out Tests of Significance for means and proportions Here are the data for the situations in Part 1. Use them to answer the questions below. 1. * = 6.71 s = 1. 62 2. Of the 40 employees selected, 12 were female 3. X =8.2 s = 1.62 4. * = $101.20 s =$12.65 5. 11 of the 400 packages tracked were misrouted 6. X =26.3 s = 5.72 7. X =9.4 s = 0.43 8. * = 10.21 s = 1.25 9. Gun control was important to 855 of the 1525 Americans sampled. 1. Use the data above to perform the test from number 9 in Part I. Be sure to indicate your P-value and your conclusion. State your conclusion in the context of the problem using normal English. P-value = Conclusion (circle one): Reject Ho Fail to Reject Ho Conclusion in Context: 2. Use the data to perform the test from number 6 in Part I. Be sure to indicate your P-value and your conclusion. State your conclusion in the context of the problem using normal English. P-value = Conclusion (circle one): Reject Ho Fail to Reject Ho Conclusion in Context: 3. Find the P-values in the other 7 problems. Circle (or highlight in red) the ones that indicate strong evidence that the null is false. Draw squares around (or highlight in blue) questionable P-values for which you would need to know the significance level in order to make a decision. Number 1: Number 2: Number 3: Number 4: Number 5: Number 7: Number 8