1- Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. Consider drawing a random sample of n= 5 stocks from the population of all stocks and calculating the mean return, x, of the sampled stocks. Find the mean and the standard deviation of the sampling distribution of x, and find an interval containing 95.44 percent of all possible sample mean returns.
2- In the July 29,2001, issue of the Journal News (Hamilton, Ohio) Lynn Elber of the Associated Press reported on a study conducted by the Kaiser Family Foundation regarding parents’ use of television set V-chips for controlling their children’s TV viewing. The study asked parents who own TVs equipped with V-chips whether they use the devices to block programs with objectionable content.
a. Suppose that we wish to use the study results to justify the claim that fewer than 20 percent of parents who own TV sets with V-chips use the devices. The study actually found that 17 percent of the parents polled used their V-chips. If the poll surveyed 1,000 parents, and if for the sake of argument we assume that 20 percent of parents who own V-chips actually use the devices (that is, p = .2), calculate the probability of observing a sample proportion of .17 or less. That is, calculate P(∧p≤ .17). (**The ^symbol is on top of the p; however, I cannot get word to insert the ^ symbol over the p.)
b. Based on the probability you computed in part a, would you conclude that fewer than 20 percent of parents who own TV sets equipped with V-chips actually use the devices? Explain.
3- Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is x = 50.575. If we let μ denote the mean of the breaking strengths of all possible trash bags of the new type and assume that σ equals 1.65:
a. Calculate 95 percent and 99 percent confidence intervals for μ.
b. Using the 95 percent confidence interval, can we be 95 percent confident that μ is at least 50 pounds? Explain.
c. Using the 99 percent confidence interval, can we be 99 percent confident that μ is at least 50 pounds? Explain.
d. Based on your answers to part b and c, how convinced are you that the new 30-gallon trash bag is the strongest such bag on the market?
4- Quality Progress, February 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by “listening to the voice of the customer.” A key measure of customer satisfaction is the response on a scale from 1 to 10 to the question: “Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?” Suppose that a random sample of 350 current customers results in 195 customers with a response of 9 or 10 representing “customer delight.” Find a 95 percent confidence interval for the true proportion of all current Bank of America customers who would respond with a 9 or 10. Are we 95 percent confident that this proportion exceeds .48, the historical proportion of customer delight for Bank of America?
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