Assume that the two samples are independent simple random samples selected from
ID: 3384608 • Letter: A
Question
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.Explanation / Answer
option (D)
the standard error of the difference in means in the population is>
sigma= root over( sigma1^2/ n1 + sigma2^2/n2)
=root over( sigma1^2((1/n1) + (1/n2)) [as popln std dev.s are equal]
=root( sigma1^2 *( 1/11+ 1/9))
now sigma1^2 is estimated by=(s1^2 + s2^2)/2 =((3.4)^2 + (3.7)^2 )/2 =12.625
so,sigma = root ( 12.625*(1/11 +1/99) ) = 1.597
d.f=(n1-1)+(n2-1)= 18
t-value at 99% conf int. with (df=18) = 2.878
so,conf. int.= [ ( 70.3 -67.8) - (2.878*1.597),( 70.3 -67.8) - (2.878*1.597) ]
which nearly equals to = [ 2.07 ,7.07 ]