[1] When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.00 lb. (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger, et al.,Journal of the American Medical Association, Vol. 293, No. 1). Assume that the standard deviation of all such weight changes iss = 4.9 lb. We shall use a 0.01 significance level to test the claim that the mean weight loss is greater than 0.
a)Set up the null and alternative hypotheses, and perform the hypothesis test.
b)Based on these results, does the diet appear to be effective?
c)Does the diet appear to have practical significance?
[2] An earlier study claims that U.S. adults spend an average of 114 minutes with their families per day. A recently taken sample of 25 adults showed that they spend an average of 109 minutes per day with their families. The sample standard deviation is 11 minutes. Assume that the time spent by adults with their families has an approximate normal distribution. We wish to test whether the mean time spent currently by all adults with their families is less than 114 minutes a day.
a)Set up the null and alternative hypotheses, and perform the hypothesis test with a significance level of 0.05.
b)Does the sample information support that the mean time spent currently by all adults with their families is less than 114 minutes a day? Explain your conclusion in words.
[3] A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. We shall use a 0.05 significance level to test the claim that a family of four will spend more money, on average, when vacationing at Niagara Falls per day than the average amount for a family of four claimed by the American Automobile Association.
a)Set up the null and alternative hypotheses, and perform the hypothesis test.
b)Based on the confidence interval from part a), does it appear that the population mean amount spent per day by families visiting Niagara Falls is more than the mean reported by the American Automobile Association? Explain.
[4] In the case ofCastenedav.Partida, 1977, it was found that during a period of 11 years in Hilda County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. We shall use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry.
a)Set up the null and alternative hypotheses, and perform the hypothesis test.
b)Does the jury selection system appear to be fair?
[5] A bakery in my neighborhood produces loaves of bread with “1 pound” written on the label. Weights of randomly selected sampled loaves from today’s production were recorded below:
| 1.02 | 0.97 | 0.98 | 1.04 | 1.00 | 1.02 | 0.98 | 1.03 |
| 1.03 | 0.99 | 1.02 | 1.06 | 0.95 | 1.01 | 0.97 | 1.02 |
a)If you are to perform a hypothesis test to test the claim on the label that the mean weight of the entire loaves of bread production is more than “1 pound,” what distribution are you going to apply and explain why?
b)If an average weight is less than or equal to “1 pound,” then customers think that the bakery is taking advantage of its weight. When customers find out its actual weight, they might certainly complain about it. Use a 0.05 significance level to test the claim that the mean weight of the entire loaves of bread production is more than “1 pound.”
c)Do you think that the bakery is correct in its label claim?
[6] On January 7, 2000, the Gallup Organization released the results of a poll comparing lifestyles of today with that yesteryear. Then poll results were based in telephone interviews with a randomly selected national sample of 1,031 adults, 18 years and older, conducted December 20-21, 1999. One question asked if the respondent had vacationed for six days or longer within the last 12 months. Suppose that we will attempt to use the poll’s results to justify the claim that more than 40 percent of U.S. adults have vacationed for six days or longer within the last 12 months. The poll actually found that 42 percent of the respondents had done so. Would you conclude that more than 40 percent of U.S. adults have vacationed for six days or longer within the last 12 months? Explain.
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