Question

Having the worst time trying to answer these three questions below.

Assume that σ21=σ22=σ2. Calculate the pooled estimator of σ2 when the first sample gives s21=128 and the second independent sample gives s22= 128, and n1=n2=36. Give your answer to two decimal places , do not round up or down.

And ..

Two independent random samples have been slected ; 111 observations from population one and 143 observations from population two. From previous experience it is known that the standard deviations are

σ1=3{"version":"1.1","math":"\sigma_{1}=3"}

and

σ2=4{"version":"1.1","math":"\sigma_{2}=4"}

.

Suppose the sample mean is 28.1 for the sample from population one and the sample mean is 13.3 from population two.

Suppose you wish to test the hypothesis

Ho:(μ1−μ2)=0{"version":"1.1","math":"H_{o}:\left(\mu_{1}-\mu_{2}\right)=0"}

versus

Ho:(μ1−μ2)≠0{"version":"1.1","math":"H_{o}:\left(\mu_{1}-\mu_{2}\right)\neq0"}

what woud be the value of the test statistic. Give answer to two decimal places.

And..

A company makes two types of paint. Independently a samples of paint from each type of paint was used and drying times recorded. Let D = [ ( sample average for sample one ) - ( sample average for sample two) ] .

The sample sizes were n1=17 and n2 = 12 .

We assumed that the two populations ( paint drying times for the two types of paint) have equal variances .

For the samples taken, D =2.9 and the pooled sample estimator of the common (equal ) population variance is (s_p)^2₌( 4.8)(4.8) . That is Sp = 4.8

Construct a 95% confidence interval estimate for the difference in the two population means (type 1 paint versus type 2 paint) or

μ1−μ2{"version":"1.1","math":"\mu_{1}-\mu_{2}"}

For your answer give the width of your confidence interval , to two decimal places , do not round up or down.

Answer 1