Question

Given two independent random samples with the following results:

n1	=	8		n2	=	6
xbar1	=	153		xbar^2	=	177
s1	=	22		s2	=	17

Use this data to find the 90% 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 90% confidence interval. Round your answers to the nearest whole number. Both lower and upper endpoint.

Answer 1

solution:-
Step 1 of 3:-
given that n1 + n2 = 8 + 6 = 14
df = ( n1 + n2)-2 = 14 - 2 = 12
then 90% confidence with df = 12 is t = 1.782

Step 2 of 3:-
standard error formula
=> sqrt((s1^2/n1)+(s2^2/n2))
=> sqrt((22^2/8)+(17^2/6))
=> 10

Step 3 of 3:-
confidence interval formula
=> (x1 - x2) +/- t * sqrt((s1^2/n1)+(s2^2/n2))
=> (153 - 177) +/- 1.782 *10
=> -24 +/- 17.82
=> (-42 , -6)