Question

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Construct a 99% confidence interval for mu1 - mu2, the difference between the mean drying time for paint type A and the mean drying time for paint type B.

Answer 1

Ans.

The given question is the case of Two sample t-test with EQUAL VARIANCE. As given in the question that the population standard deviation are equal, so we can assume to conduct a two sample t-test with Equal Variance. As there are two independent samples Type A with number, and Type B with number .

Lets suppose the mean drying time for type A :

and mean drying time for Type B :

Now we have to find the 99% confidence interval for difference of mean of drying time for two population

The formula to calculate the confidence interval is:

where,

pooled variance,   

    Standard error for the difference in mean when assuming equal variance.

99% confidence interval for difference in mean of two population for this we have

Interpretation of this confidence interval is that, "We are 99% confident that the interval contains the true mean difference of drying time for type A and Type B can."