Question

In order to estimate the difference between the average mortgages in the southern and the northern states of the United States, the following information was gathered.

	South	North
Sample Size	40	45
Sample Mean (in $1,000)	$170	$175
Sample Standard Deviation (in $1,000)	$5	$7

a.	Compute the degrees of freedom for the t distribution.
b.	Develop an interval estimate for the difference between the average of the mortgages in the South and North. Let Alpha = 0.03.

Answer 1

Part a)

DF = 79

Part b)

Confidence interval :-



Lower Limit =
Lower Limit = -7.8932
Upper Limit =
Upper Limit = -2.1068

97% Confidence interval is ( -7.8932 , -2.1068 )

We are 97% confident that the average of the mortgages in the South and North lies within the interval  ( -7.8932 , -2.1068 ).