Construct the indicated confidence interval for the difference between the two p

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 (o1=o2), so that the standard error of the difference between means is obtained by pooling variances. Q) 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. Type A x1 = 70.7 hrs s1 = 3.8 hrs n1 = 11 Type B: x2 = 68.6 hrs s2 = 3.6 hrs n2 = 9 Construct a 99% confidence interval for µ1 - µ2, the difference between the mean drying time for paint of type A and the mean drying time for paint of type B.

Explanation / Answer

Type A x1 = 70.7 hrs s1 = 3.8 hrs n1 = 11

Type B: x2 = 68.6 hrs s2 = 3.6 hrs n2 = 9

z value at 99% CI = 2.576

CI = ( x1 - x2) + /- z * sqrt(s1^2 / n1 + s2^2 /n2)

= ( 70.7 - 68.6) + / - 2.576 *sqrt( 3.8^2 / 11 + 3.6^/9)

= (-2.174 , 6.374)

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