Determine the 95% confidence interval for the difference between two population means where sample 1 has data: 16,14,19,18,19,20,15,18,17,18,and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.(Assume equal population variances)
A)(-0.16 4.76)
B)(-0.58 5.18)
C)(0.01 4.59)
D)(0.56 4.04)

Question

Quizplus · Accepted Answer

The correct answer is A because the 95% confidence interval for the difference between two population means is (-0.16, 4.76). This can be calculated using the formula:CI = (x̄1 - x̄2) ± t*√(s1^2/n1 + s2^2/n2)where x̄1 and x̄2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t is the t-value for the desired confidence level and degrees of freedom.In this case, we have:x̄1 = 17.5x̄2 = 15.3s1 = 2.24s2 = 3.46n1 = 11n2 = 10df = 19Using a t-table, we find that the t-value for a 95% confidence level and 19 degrees of freedom is 2.093.Plugging these values into the formula, we get:CI = (17.5 - 15.3) ± 2.093*√(2.24^2/11 + 3.46^2/10)CI = 2.2 ± 2.38CI = (-0.16, 4.76)

Determine the 95% Confidence Interval for the Difference Between Two