Questions on the topic: two means independent sampling
1.Assume that σ21=σ22=σ2. Calculate the pooled estimator of σ2 when the first sample gives s21=125 and the second independent sample gives s22= 126, and n1=n2=25. Give your answer to two decimal places , do not round up or down.
2.
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 =2.1 and the pooled sample estimator of the common (equal ) population variance is (sp)2 =( 4.0)(4.0) .
Construct a 95% confidence interval estimate for the difference in the two population means (type 1 paint versus type 2 paint) or
μ1−μ2
.
For your answer give the width of your confidence interval , to two decimal places , do not round up or down.

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