The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say their ColorSmart-5000 television sets did not need a repair, whereas 84 say their ColorSmart-5000 television sets did need at least one repair. (a) Find a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years without needing a single repair. (Round your answers to 3 decimal places.) The 99 percent confidence interval is 1. (b) Does this confidence interval provide strong evidence that the percentage of all ColorSmart- 5000 television sets that last at least five years without a single repair is less than the 95 percent claimed by the manufacturer? Yes , the interval is below 0.95.Consumer Reports (January 2005) indicates that prot margins on extended warranties are much greater than on the purchase of most products. In this exercise we consider a major electronics retailer that wishes to increase the proportion of customers who buy extended warranties on digital cameras. Historically, 20 percent of digital camera customers have purchased the retailer's extended warranty. To increase this percentage, the retailer has decided to offer a new warranty that is less expensive and more comprehensive. Suppose that three months after starting to offer the new warranty, a random sample of 535 customer sales invoices shows that 169 out of 535 digital camera customers purchased the new warranty. Find a 95 percent condence interval for the proportion of all digital camera customers who have purchased the new warranty. Are we 95 percent condent that this proportion exceeds .20? (Round your answers to 3 decimal places.) The 95 percent oonfdence Interval is _ ]. Consumer Reports {January 2005) indicates that prot margins on extended warranties are much greater than on the purchase of most products. In this exercise we consider a major electronics retailer that wishes to increase the proportion of customers who buy extended warranties on digital cameras. Historically, 20 percent of digital camera customers have purchased the retailer's extended warranty. To increase this percentage, the retailer has decided to offer a new warranty that is less expensive and more comprehensive. Suppose that three months after starting to offer the new warranty. a random sample of 504 customer sales invoices shows that 156 out of 504 digital camera customers purchased the new warranty. Find a 95 percent condence interval for the proportion of all digital camera customers who have purchased the new warranty. Are we 95 percent condent that this proportion exceeds .20? (Round your answers to 3 decimal places.) .QEWEmgag ____________________________________________________________ 1. Recall that the cigarette industry requires that models in cigarette ads must appear to be at least 25 years old. Also recall that a sample of 50 people is randomly selected at a shopping mall. Each person in the sample is shown a "typical cigarette ad" and is asked to estimate the age of the model in the ad. The pvalue for testing Ho versus Ha can be calculated to be 0.0048. Determine whether Ho would be rejected at each of a = .10, a = .05, a = .01, and a = .001. {Round your answer to 4 decimal places.) Reject H0 at u = The HR department tested how long employees stay with the company in their current positions. A random sample of 50 employees yielded a mean of 2.79 years and o= .76. The sample evidence indicates that the average time is less than 3 years and is significant at a = .01. True or False True FalseThe bank manager wants to show that the new system reduces typical customer waiting times to less than 6 minutes. One way to do this is to demonstrate that the mean ofthe population of all customer waiting times is less than 6. Letting this mean be ,u, in this exercise we wish to investigate whether the sample of 108 waiting times provides evidence to support the claim that ,u is less than 6. For the sake of argument, we will begin by assuming that ,u equals 6, and we will then attempt to use the sample to contradict this assumption in favor ofthe conclusion that ,u is less than 6. Recall that the mean ofthe sample of 108 waiting times is f = 5.51 and assume that O, the standard deviation of the population of all customer waiting times. is known to be 2.24. (a) Consider the population of all possible sample means obtained from random samples of 108 waiting times. What is the shape of this population of sample means? That is, what is the shape of the sampling distribution off ? Normal because the sample is arge (In) Find the mean and standard deviation of the population of all possible sample means when we assume that p equals 6. (Round your answer to 4 decimal places.) pY=6,dY= (c) The sample mean that we have actually observed is i = 5.51. Assuming that u equals 6, nd the probability of observing a sample mean that is less than or equal to i = 5.51. (Round "z-value" to 2 decimals and final answer to 4 decimal places.) PR