Question

Given two independent random samples with the following results:

n 1 =8x ‾  1 =89s 1 =19  n1=8x‾1=89s1=19    n 2 =11x ‾  2 =128s 2 =28  n2=11x‾2=128s2=28

Use this data to find the 90% 90% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed.

n1 8, n2 11, x1 89, x2 128, s1 19, s2 28

Step 2 of 3 :

Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Answer 1

solution:-

step 1 of 3:

point estimate = x1-x2 = 89 - 128 = -39

step 2 of 3:

margin of error

degree of freedom df = (n1+n2)-2 = (8+11)-2 = 17

we look into t table with df and probability of (1-0.90) is 0.10

critical value t = 1.740

margin of error formula

=> t * sqrt(s1^2/n1 + s2^2/n2)

=> 1.740 * sqrt((19^2/8) + (28^2/11))

=> 18.772473

step 3 of 3:

confidence interval

=> point estimate +/- margin of error

=> -39 +/- 18.772473

=> (-57.77 , -20.23) rounded to two decimals