
A pharmaceutical firm is interested in the efficacy of a new drug and of a standard drug. The research division of the firm randomly selects two groups of volunteers. One group is given the new drug and the other group is given the standard drug. Data are recorded on the effects of each drug. Is the research division using dependent or independent samples? Why?

A production manager wishes to determine if there is a difference in the number of production runs produced by the night shift and the day shift. A random sample of night and day shifts is selected, and the number of production units for each shift is recorded. The following are the results of the same:

sigma
n
Day Shift
27.4
6.4
60
Night Shift
18.3
5.9
60

Find a 90% confidence interval on the difference in the mean number of production units for the two shifts.

Calculate a 99% confidence interval for part a)

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 statistics calculated:
Sample 1: n_{1} = 12, = 10, s_{1} = 2.04; Sample 2: n_{2} = 15, = 12, s_{2} = 1.4

Find a 90% confidence interval for µ_{1} – µ_{2} using the pooled estimate of the variance for the populations.
4) A restaurant owner is interested in determining whether there is any difference in the weekly sales of his restaurants at two locations. The weekly sales are normally distributed. The sales, in dollars, for seven randomly selected weeks are:
Week 
Restaurant 1 
Restaurant 2 
1 
4100 
3800 
2 
1800 
4600 
3 
2200 
5100 
4 
3400 
3050 
5 
3100 
2800 
6 
1100 
1950 
7 
2200 
3400 
Using a significance level of .01, is there evidence to support the conclusion that there is a significant difference in the weekly sales of the two restaurants?