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?2) A random sample results in 1 = 20 with n1 = 100. The population standard deviation is ?1 = 6. Another sample was selected independently resulting in 2 = 22 with n2 = 100. The population standard deviation is ?2 = 7. Test that the population means differ using a 1% significance level.3) First National Bank and City National Bank are competing for customers who would like to open IRAs. Thirty two weeks are randomly selected for First National Bank and another 32 weeks are randomly selected for City National Bank. The total amount deposited into IRAs is noted for each week. A summary of data (deposits in thousands of dollars) from the survey is as follows: First National 1 = 4.1, ?1 = 1.2; City National 2 = 3.5, ?2 = 0.9. Use a 98% confidence interval to estimate the difference in the mean weekly deposits into IRAs for each bank.4) 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: ?nDay Shift27.46.460Night Shift18.35.960a) Find a 90% confidence interval on the difference in the mean number of production units for the two shifts.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).
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