Question

Given two independent random samples with the following results: n₁=6, x‾₁=132 (line goes over the x), s₁=29, n₂=10 x‾₂=116 (line goes over the x), s₂=31

Use this data to find the 95% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3:

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3:

Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to the nearest whole number.

Step 3 of 3:

Construct the 95% confidence interval. Round your answers to the nearest whole number.

Answer 1

Step 1

Critical value    t(α/2, n1 + n1 - 2) = t( 0.05/2, 6 + 10 - 2) = 2.145

Step 2

Standard Error = SP / √( (1/n1) + (1/n2)) = 58.6774 ≈ 59

Step 3

Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))
t(α/2, n1 + n1 - 2) = t( 0.05/2, 6 + 10 - 2) = 2.145

( 132 - 116 ) ± t(0.05/2 , 6 + 10 -2) 30.3009 √ ( (1/6) + (1/10))
Lower Limit = ( 132 - 116 ) - t(0.05/2 , 6 + 10 -2) 30.3009 √( (1/6) + (1/10))
Lower Limit = -17.5635 ≈ -18
Upper Limit = ( 132 - 116 ) + t(0.05/2 , 6 + 10 -2) 30.3009 √( (1/6) + (1/10))
Upper Limit = 49.5635 ≈ 50
95% Confidence Interval is ( -18 , 50 )