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# Math 104 - Spring ‘14-Applied Regression Analysis Exam Solution

Question # 00009970
Subject: Mathematics
Due on: 03/12/2014
Posted On: 03/10/2014 11:02 PM

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[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 is ? = 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? 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] In March 16, 1998, issue of Fortune magazine, the results of a survey of 2,221 MBA students from across the United States conducted by the Stockholm-based academic consulting firm Universum showed that only 20 percent of MBA students expect to stay at their first job five years or more. Source: Shalley Branch, "MBAs: What Do They Really Want," Fortune (March 16, 1998), p.167.
a) Set up the null and alternative hypotheses to test whether the proportion of MBA students who expect to stay at their first job five years or more is less than one-fourth of all U.S. MBA students.
b) Perform the hypothesis test with a significance level of 0.02.
c) Based on the interval from b), can you conclude that there is strong evidence that less than one-fourth of all U.S. MBA students expect to stay? Explain why.

[4] In the case of Casteneda v. 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 wine manufacturer sells cabernet with a label that asserts an alcohol content of 11%. Sixteen bottles of this label are randomly selected and analyzed for alcohol content. The resulting observations are:
10.8 9.6 9.5 11.4 9.8 9.1 10.4 10.7
10.2 9.8 10.4 11.1 10.5 10.8 9.5 9.8
Looking at the data, you suspect that the manufacturer is incorrect in its label claim. You want to perform hypothesis testing to prove or disprove it.
a) Do you think that it is possible to perform hypothesis test on this case? Explain.
b) Do you think that the manufacturer is correct in its label claim? Explain.

[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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#### Math 104 - Spring ‘14-Applied Regression Analysis Exam Solution

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Posted On: 03/10/2014 11:04 PM
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Preview: = xxx – xxxxxx D /sqrt(n))U1= xxxxxx meanU2= Population xxxxx D x xxxxxxx deviationn=sample xxxxxxxxxxx =109 minutesU2 x 114 minutesS x = xx xxxxxxx n= xxxxxxxx 05now, T x -5*(?25)/11 T x -2 xxxxxxxxxxxx x TCritical x Talpha,n-1 = xx 05,24 =2 xxxxxxxx Null xxxxxxxxxx xx T xxxx - T0 xxxxx (-2 27 xxxx -2 xxxxxxxxxx xxxx hypothesis xx rejected at x % significance xxxxx which xxxxx xxxxxx spend xxxx than 114 xxxxxxx per day xxxxx tailed xxxxxxx x 034 xxxx 5 %Which xxxxxx means on xxxxx of xx xxxxx we xxxxxx the null xxxxxxxxxx b) Confidence xxxxxxxxxxxxxxxxxx interval xx xxxxx by x I = xxxxxxxxxxxxx D /?n), xxxxxxxxxxxx D xxxxx x (109-2 xxxx 2,109+2 06*2 xx = (104 xxxxxx 54)Now xx xxx say xxxx We are 95% confident that the true mean is less than 114 minutes a day therefore, we are also 95%  confident that the sample information supports the claim xxx In March xxx 1998, xxxxx xx Fortune xxxxxxxxx the results xx a survey xx 2,221 xxx xxxxxxxx from xxxxxx the United xxxxxx conducted by xxx Stockholm-based xxxxxxxx xxxxxxxxxx firm xxxxxxxxx showed that xxxx 20 percent xx MBA xxxxxxxx xxxxxx to xxxx at their xxxxx job five xxxxx or xxxx xxxxxxx Shalley xxxxxxx "MBAs: What xx They Really xxxxxx Fortune xxxxxx xxx 1998), x 167 a) xxx up the xxxx and xxxxxxxxxxx xxxxxxxxxx to xxxx whether the xxxxxxxxxx of MBA xxxxxxxx who xxxxxx xx stay xx their first xxx five years xx more xx xxxx than xxxxxxxxxx of all x S MBA xxxxxxxx b) xxxxxxx xxx hypothesis xxxx with a xxxxxxxxxxxx level of x 02 xx xxxxx on xxx interval from xxx can you xxxxxxxx that xxxxx xx strong xxxxxxxx that less xxxx one-fourth of xxx U x xxx students xxxxxx to stay? xxxxxxx why Solution xx and xxxxxx xxxxxxxxxx proportion x 0 25 xxx n = xxxxxx the xxxxxxxxxx x Ÿ xxxxxxxxxx proportion = xxxxxxxxx 25) = xxx 25 x x and x Ÿ (1 xxxxxxxxxxxxx proportion) = xxxxxxx – x xxx = xxxxx 75 ? x So, we xxx use xxx xxxxxx distribution xx approximate a xxxxxxxx distribution The xxxx hypotheses xx x the xxxxxxxxxx of all x S MBA xxxxxxxx who xxxxxx xx stay xx their first xxx five years xx more xx xxxxx (.....
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