Question

Assume that you have a sample of n1=7​, with the sample mean Upper X overbar 1 =41​, and a sample standard deviation of Upper S 1 = 4​, and you have an independent sample of n2=12 from another population with a sample mean of Upper X overbar 2 =35​, and the sample standard deviation Upper S 2 =6.Construct a 90​% confidence interval estimate of the population mean difference between μ1 and μ2. Assume that the two population variances are equal.

Answer 1

Mean1 () = 41

Sample size1 (n1) = 7 Standard deviation1 (s1) = 4 Mean2 () = 35

Sample size2 (n2) = 12 Standard deviation2 (s2) = 6 Confidence interval(in %) = 90

Degree of freedom = 12 + 7 - 2 = 17

Since we know that

Required confidence interval = (6.0-4.4509, 6.0+4.4509)

Required confidence interval = (1.5491, 10.4509)

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