# STAT Misc. Problems……………………..

Question1) A pharmaceutical firm is interested in the efficacy of a new drug and of a standard drug. The researchdivision of the firm randomly selects two groups of volunteers. One group is given the new drug and theother group is given the standard drug. Data are recorded on the effects of each drug. Is the researchdivision using dependent or independent samples? Why?2) A production manager wishes to determine if there is a difference in the number of production runsproduced by the night shift and the day shift. A random sample of night and day shifts is selected, and thenumber of production units for each shift is recorded. The following are the results of the same:xDay ShiftNight Shiftsigma6.45.927.418.3n6060a) Find a 90% confidence interval on the difference in the mean number of production units for the twoshifts.b) Calculate a 99% confidence interval for part a)c) Compare the length of the intervals of the two confidence intervals obtained in a) and b).3) Independent random samples were collected from two populations and the following statisticscalculated:Sample 1: n1 = 12, x1= 10, s1 = 2.04; Sample 2: n2 = 15, x 2 = 12, s2 = 1.4a) Find a 90% confidence interval for Âµ1 – Âµ2 using the pooled estimate of the variance for the populations.b) Find a 90% confidence interval for Âµ1 – Âµ2 not assuming that the population variances are equal.4) A restaurant owner is interested in determining whether there is any difference in the weekly sales ofhis restaurants at two locations. The weekly sales are normally distributed. The sales, in dollars, for sevenrandomly selected weeks are:Week1234567Restaurant 14100180022003400310011002200Restaurant 23800460051003050280019503400Using a significance level of .01, is there evidence to support the conclusion that there is a significantdifference in the weekly sales of the two restaurants?
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# STAT Misc. Problems……………………..

Question1) A pharmaceutical firm is interested in the efficacy of a new drug and of a standard drug. The researchdivision of the firm randomly selects two groups of volunteers. One group is given the new drug and theother group is given the standard drug. Data are recorded on the effects of each drug. Is the researchdivision using dependent or independent samples? Why?2) A production manager wishes to determine if there is a difference in the number of production runsproduced by the night shift and the day shift. A random sample of night and day shifts is selected, and thenumber of production units for each shift is recorded. The following are the results of the same:xDay ShiftNight Shiftsigma6.45.927.418.3n6060a) Find a 90% confidence interval on the difference in the mean number of production units for the twoshifts.b) Calculate a 99% confidence interval for part a)c) Compare the length of the intervals of the two confidence intervals obtained in a) and b).3) Independent random samples were collected from two populations and the following statisticscalculated:Sample 1: n1 = 12, x1= 10, s1 = 2.04; Sample 2: n2 = 15, x 2 = 12, s2 = 1.4a) Find a 90% confidence interval for Âµ1 – Âµ2 using the pooled estimate of the variance for the populations.b) Find a 90% confidence interval for Âµ1 – Âµ2 not assuming that the population variances are equal.4) A restaurant owner is interested in determining whether there is any difference in the weekly sales ofhis restaurants at two locations. The weekly sales are normally distributed. The sales, in dollars, for sevenrandomly selected weeks are:Week1234567Restaurant 14100180022003400310011002200Restaurant 23800460051003050280019503400Using a significance level of .01, is there evidence to support the conclusion that there is a significantdifference in the weekly sales of the two restaurants?
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