An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. 2023 Business Finance
2023 1 An experiment was designed to estimate the mean difference in weight
1) An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences μ_{d}, where d = ration A – ration B. (Give your answers correct to two decimal places.)
Litter 
1 
2 
3 
4 
5 
6 
7 
8 

Ration A 
39 
58 
58 
46 
52 
60 
47 
49 

Ration B 
48 
52 
38 
42 
58 
39 
42 

Lower Limit: _________ 






Upper Limit: _________
2) Consider the following hypothesis test for the mean difference. (Give your answers correct to four decimal places.) (a) Determine the pvalue for H_{o}: μ_{d} = 0 and H_{a}: μ_{d} > 0, with n = 16 and t = 1.99. (b) Determine the pvalue for H_{o}: μ_{d} = 0 and H_{a}: μ_{d} ≠ 0, with n = 24 and t = 1.93. (c) Determine the pvalue for H_{o}: μ_{d} = 0 and H_{a}: μ_{d} < 0, with n = 34 and t = 2.67. (d) Determine the pvalue for H_{o}: μ_{d} = 0.75 and H_{a}: μ_{d} > 0.75, with n = 15 and t = 3.47.
3) Ten randomly selected college students, who participated in a learning community, were given pre–selfesteem and post–selfesteem surveys. A learning community is a group of students who take two or more courses together. Typically, each learning community has a theme, and the faculty involved coordinate assignments linking the courses. Research has shown that the benefits of higher selfesteem, higher grade point averages (GPAs), and improved satisfaction in courses, as well as better retention rates, result from involvement in a learning community. The scores on the surveys are as follows.
Does this sample of students show sufficient evidence that selfesteem scores were higher after participation in a learning community? Lower scores indicate higher selfesteem. Use the 0.05 level of significance and assume normality of scores. (a) Find t. (Give your answer correct to two decimal places.) (ii) Find the pvalue. (Give your answer correct to three decimal places.)
Faa) Fail to reject H_{0}. At the 0.05 level of significance, there is sufficient evidence to show that one’s self esteem increases after participation in a learning community. b) b) Reject H_{0}. At the 0.05 level of significance, there is insufficient evidence to show that one’s self esteem increases after participation in a learning community. c) Reject H_{0}. At the 0.05 level of significance, there is sufficient evidence to show that one’s self esteem increases after participation in a learning community. d) Fail to reject H_{0}. At the 0.05 level of significance, there is insufficient evidence to show that one’s self esteem increases after participation in a learning community.



4) A study comparing attitudes toward death was conducted in which organ donors (individuals who had signed organ donor cards) were compared with nondonors. Templer’s Death Anxiety Scale (DAS) was administered to both groups. On this scale, high scores indicate high anxiety concerning death. The results were reported as follows.
n 
Mean 
Std. Dev. 

Organ Donors 
28 
5.09 
2.75 
Nonorgan Donors 
74 
7.24 
3.38 
Construct the 95% confidence interval for the difference between the means, μ_{non} − μ_{donor}. (Estimate df by using the smaller value of df_{donor} and df_{non}.)
lower limit: __________ 

upper limit: __________
5) If a random sample of 24 homes south of Center Street in Provo has a mean selling price of $145,375 and a standard deviation of $4750, and a random sample of 24 homes north of Center Street has a mean selling price of $148,600 and a standard deviation of $5900, can you conclude that there is a significant difference between the selling price of homes in these two areas of Provo at the 0.05 level? Assume normality. (a) Find t. (Give your answer correct to two decimal places.) (ii) Find the pvalue. (Give your answer correct to four decimal places.)
(b) State the appropriate conclusion. (choose one) Re a) Reject the null hypothesis, there is not significant evidence of a difference in means. b) Reject the null hypothesis, there is significant evidence of a difference in means. c) Fail to reject the null hypothesis, there is significant evidence of a difference in means. d) Fail to reject the null hypothesis, there is not significant evidence of a difference in means.
6) A study titled “Factors Leading to Reduced Intraocular Pressure after Combined Trabeculotomy and Cataract Surgery” in the Journal of Glaucoma investigated the influence cataract surgery alone and cataract surgery with trabeculotomy has on eye pressure. Two groups were formed for each type of surgery and were compared for similarities with respect to several factors beforehand. No significant difference was found between the two groups with respect to the number of preoperative glaucoma medications the patient was taking. Suppose a similar study involving six patients receiving the combined surgery and five patients receiving the cataract surgery alone produced the following values of number of medications. Using the MannWhitney U test, determine whether the two groups are the same with respect to number of medications. Use α = .05.
(a) Find U. (ii) Find the critical Uvalue.
(b) State the appropriate conclusion. (choose one) Re a) Reject the null hypothesis, there is significant evidence that the number of medications differ. b) Reject the null hypothesis, there is not significant evidence that the number of medications differ. c) Fail to reject t1) An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences μ_{d}, where d = ration A – ration B. (Give your answers correct to two decimal places.)
4) A study comparing attitudes toward death was conducted in which organ donors (individuals who had signed organ donor cards) were compared with nondonors. Templer’s Death Anxiety Scale (DAS) was administered to both groups. On this scale, high scores indicate high anxiety concerning death. The results were reported as follows.
Construct the 95% confidence interval for the difference between the means, μ_{non} − μ_{donor}. (Estimate df by using the smaller value of df_{donor} and df_{non}.)
he null hypothesis, there is significant evidence that the number of medications differ. d) Fail to reject the null hypothesis, there is not significant evidence that the number of medications differ.

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