Question

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A​ (the original​ paint) and 9 cans of type B​ (the modified​ paint) were selected and applied to similar surfaces. The drying​ times, in​ hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following​ 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2​, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population​ means? 4.90 hrless than

Answer 1

This question is incomplete. I got the complete part (the boldened part) of it from google as:

The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:

4.90 hrs < μ1 - μ2 < 17.50 hrs.

Answer:

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A​ (the original​ paint) and 9 cans of type B​ (the modified​ paint) were selected and applied to similar surfaces. The drying​ times, in​ hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following​ 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2​, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population​ means?

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Step-by-step explanation:

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.