Question

Given two independent random samples with the following results:

n1	=	11		n2	=	13
xbar1	=	162		xbar^2	=	130
s1	=	31		s2	=	30

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.

Copy Data

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. Both lower and upper endpoint.

Answer 1

The population variances are equal.

So we have to use here pooled variance.

Step1:

Degrees of freedom = n1 + n2 - 2 = 11 + 13 - 2 = 22

Level of significance = 0.05

Critical value = tc = 2.074 ( From t table)

Step 2:

Standard error is SE

Step 3:

We have to construct 95% confidence interval for the difference between means.

Formula is

E = tc*SE = 2.074*12.4781 = 25.8780

( 32 - 25.8780 , 32 + 25.8780) = > ( 6.1220 , 57.8780) = > ( 6 , 58)