b. In the automobile parts supplier's hypothesis test of Ho : M= 3 versus Ha: # # 3, find the sample size needed to make the probability of a Type I error equal to .05 and the probability of a Type II error corresponding to the alternative value pa = 3.005 equal to .05. Here, assume o equals .023. (Round your answer up to the nearest whole number.) nSuppose that a national survey finds that 73 percent of restaurant employees say that work stress has a negative impact on their personal lives. A random sample of 200 employees of a large restaurant chain nds that 141 employees say that work stress has a negative impact on their personal lives. (a) Formulate the null and alternative hypotheses needed to attempt to provide evidence that the percentage of work-stressed employees for the restaurant chain differs from the national percentage. (b) Use critical values and a p-value to perform the hypothesis test by setting 0 equal to .10, .05, .01, and .001. (Negative value should be indicated by a minus sign. Round p-value to 4 decimal places and z to 2 decimal places.) A consumer electronics firm has developed a new type of remote control button that is designed to operate longer before becoming intermittent. A random sample of 35 of the new buttons is selected and each is tested in continuous operation until becoming intermittent. The resulting lifetimes are found to have a sample mean of Tc =1,240.8 hours and a sample standard deviation of s = 109.8. (a) Independent tests reveal that the mean lifetime (in continuous operation) of the best remote control button on the market is 1,200 hours. Letting u be the mean lifetime of the population of all new remote control buttons that will or could potentially be produced, set up the null and alternative hypotheses needed to attempt to provide evidence that the new button's mean lifetime exceeds the mean lifetime of the best remote button currently on the market. (b) Using the previously given sample results, use critical values to test the hypotheses you set up in part a by setting 0 equal to .10, .05, .01, and .001. What do you conclude for each value of a? (Round your answers to 3 decimal places.) (c) Suppose that 7c = 1,240.8 and s=109.8 had been obtained by testing a sample of 100 buttons. Use critical values to test the hypotheses you set up in part a by setting 0 equal to .10, .05, .01,and .001. Which sample (the sample of 35 or the sample of100) gives a more statistically signicant result? That is, which sample provides stronger evidence that Ha is true? (Round your answers to 3 decimal places.) H0 at each value of a. Sample of n = 100 provides stronger evidence. Consolidated Power, a large electric power utility, hasjust built a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environmental Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal pollution of the marine environment near the plant can be avoided. Because of this order, the waste water is allowed to cool in specially constructed ponds and is then released into the ocean. This cooling system works properly if the mean temperature of waste water discharged is 60F or cooler. Consolidated Power is required to monitor the temperature of the waste water. A sample of100 temperature readings will be obtained each day, and if the sample results cast a substantial amount of doubt on the hypothesis that the cooling system is working properly (the mean temperature of waste water discharged is 60F or cooler), then the plant must be shut down and appropriate actions must be taken to correct the problem. (a) Consolidated Power wishes to set up a hypothesis test so that the power plant will be shut down when the null hypothesis is rejected. Set up the null hypothesis H0 and the alternative hypothesis Ha that should be used. H0=u _60versusHa=u _60 3 (b) Suppose that Consolidated Power decides to use a level of significance of a = .05, and suppose a random sample of100 temperature readings is obtained. If the sample mean of the 100 temperature readings is 7c = 61.475, test H0 versus Ha and determine whether the power plant should be shut down and the cooling system repaired. Perform the hypothesis test by using a critical value and a p-value. Assume a: 5. (Round your 2 to 2 decimal places and p-value to 4 decimal places.) Recall that "very satisfied" customers give the XYZBox video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 65 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZBox exceeds 42. Click here for the Excel Data File (a) Letting u represent the mean composite satisfaction rating for the XYZ-Box, set up the null hypothesis Ho and the alternative hypothesis Ha needed if we wish to attempt to provide evidence supporting the claim that u exceeds 42. HO: u s 42 versus Ha: p > 42 (b) The random sample of 65 satisfaction ratings yields a sample mean of f = 42.954. Assuming that 0 equals 2.64, use critical values to test Ho versus Ha at each ofo = .10, .05, .01, and .001. (Round your answer 2.05 to 3 decimal places and other z-scores to 2 decimal places.) Rejection points 20.10 20.05 20.01 70 nn1 (c) Using the information in part (b), calculate the pvalue and use it to test Ho versus H3 at each of a = .10, .05, .01, and .001. (Round your answers to 4 decimal places.) .10, 0.05, 0.01 m (d) How much evidence is there that the mean composite satisfaction rating exceeds 42? Consider a chemical company that wishes to determine whether a new catalyst, catalyst XAiOO, changes the mean hourly yield of its chemical process from the historical process mean of 750 pounds per hour. When five trial runs are made using the new catalyst, the following yields (in pounds per hour) are recorded: 801, 814,784, 836, and 820. I3 Click here for the Excel Data File (a) Let [,1 be the mean of all possible yields using the new catalyst, set up the null and alternative hypotheses needed if we wish to attempt to provide evidence that [J differs from 750 pounds. H0:u I: 750; Ha:u W '750. l (b1) The mean and the standard deviation of the sample of 5 catalyst yields are I? = 811 and s =19.647. Using a critical value and assuming approximate normality, test the hypotheses you set up in part (a) by setting 0 equal to .01. (Round your answers to 3 decimal places.) ' eject H0 at a = An airline's data indicate that 50 percent of people who begin the online process of booking a flight never complete the process and pay for the flight. To reduce this percentage, the airline is considering changing its website so that the entire booking process, including flight and seat selection and payment, can be done on two simple pages rather than the current four pages. A random sample of 300 customers who begin the booking process are exposed to the new system, and 117 of them do not complete the process. (1) Formulate the null and alternative hypotheses needed to attempt to provide evidence that the new system has reduced the noncompletion percentage. H0: p 0.5 versus Ha: p 0.5 (b) Assuming that the sample of 200 marketing researchers has been randomly selected, use critical values and the previously given sample information to test the hypotheses you set up in part a at the .10, .05, .01, and .001 levels of signicance. How much evidence is there that a majority of all marketing researchers disapprove ofthe actions taken? (Round 1?? to 4 decimal places for calculations and 2 value to 2 decimal places.) p-hat = z = 1.27 20.10 = 1 .28 Reject H0 at u = no values , nsufcient evidence. (c) Suppose a random sample of 1,000 marketing researchers reveals that 545 of the researchers disapprove of the actions taken in the conflict of interest scenario. Use critical values to determine how much evidence there is that a majority of all marketing researchers disapprove of the actions taken. (Round ? to 4 decimal places for calculations andz value to 2 decimal places.) p-hat = Z = 2.85 Z0.001 = 3.09 Reject HO at a = 0.1, 0.05, .01 and, 0.001 very strong evidence. (d) Note that in parts b and c the sample proportion ? is (essentially) the same. Explain why the results of the hypothesis tests in parts b and c differ. p-hat = 0.545 based on a much larger sample provides stronger evidence that p is greater than 0.50