Exercises. 1.The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal variances.

1. The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal variances.

; ;

; ;

Construct a 99 % confidence interval for .

2. The National Bank is interested in estimating the difference between the mean credit card balances of its two branches. Independent random samples of credit card customers provide the following results:

Branch ABranch B

Construct an interval estimate of the difference between mean balances. Use a confidence coefficient of 0.99.

3. Production quantities of two workers are shown below. Each data value indicates the amount of items produced during a randomly selected 1 day period

Worker 1: 20; 18; 21; 22; 20

Worker 2: 22; 18; 20; 23; 24

Develop a 90 % confidence interval estimate for the difference between the mean production rates of the two workers.

4. The mean salary of male professors at the universities was 54 340 tg and that of female professors was 48 080 tg. For convenience, assume that these two means are based on random samples of 28 male and 26 female professors. Assume that the standard deviations of the two samples are

3 100 tg and 2 800 tg, respectively.

Construct a 90 % confidence interval for the difference between the two population means.

5. The following summary statistics are recorded for independent random samples from two populations:

Sample 1Sample 2

Stating any assumptions that you need, determine a 98 % confidence interval for .

6. A company is interested in buying one of two different kinds of machines. Company tested the two machines for production purposes. The first machine was run for 8 hours and produced an average 123 items per hour with a standard deviation of 9 items. The second machine was run for 10 hours and produced an average of 114 items per hour with a standard deviation of 6 items. Assume that the production per hour for each machines approximately normally distributed. Also assume that the standard deviation of the hourly production of the two populations is equal.

Then find a 95 % confidence interval for the difference between the two population means.

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