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. Do not assume that the population standard deviations are equal. A paint manufacturer wished 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 Type B x1 = 75.7 hrs x2 = 64.3 hrs s1 = 4.5 hrs s2 = 5.1 hrs n1 = 11 n2 = 9

Construct a 98% 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.

A) 6.08 hrs < μ1 - μ2 < 16.72 hrs B) 5.85 hrs < μ1 - μ2 < 16.95 hrs C) 5.92 hrs < μ1 - μ2 < 16.88 hrs D) 5.78 hrs < μ1 - μ2 < 17.02 hrs

Answer 1

solution:- option B)

explanation:-

given that

type A: x1 = 75.7 hrs, s1 = 4.5 hrs, n1 = 11

type B: x2 = 64.3 hrs, s2 = 5.1 hrs, n2 = 9

degree of freedom df = (n1+n2)-2 = (11+9)-2 = 18

we look into t table with df and probability of (1-0.98) = 0.02

critical value t = 2.552

confidence interval formula

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

=> (75.7 - 64.3) +/- 2.552 * sqrt((4.5^2/11) + (5.1^2/9))

=> 5.85 < μ1 - μ2 < 16.95

=> 5.85 hrs < μ1 - μ2 < 16.95 hrs