Question

A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample​ (in years). Assume that the data come from a distribution that is Normally distributed.

Neighborhood 1: 50, 68, 65, 52, 53, 54

Neighborhood 2: 33, 32, 44, 38, 54, 51

​a) Find a 95​% confidence interval for the mean​ difference μ1- μ2​, in ages of houses in the two neighborhoods. (Round to two decimal places as needed)

​b) Is 0 within the confidence​ interval?

(Yes or No)

​c) What does the confidence interval suggest about the null hypothesis that the mean difference is​ 0?

A.Reject H0 since 0 is a plausible value for the true mean difference.

B. Fail to reject H0 since 0 is a plausible value for the true mean difference.

C.Reject H0 since 0 is not a plausible value for the true mean difference.

D.Fail to reject H0 since 0 is not a plausible value for the true mean difference.

Answer 1

First we need to find the mean and SD of both data sets. Following is the output of descriptive statistics:

Descriptive statistics
	X1	X2
count	6	6
mean	57.00	42.00
sample standard deviation	7.54	9.23
sample variance	56.80	85.20
minimum	50	32
maximum	68	54
range	18	22

(a)

(b)

No, 0 is not within the confidence interval.

(c)

C.Reject H0 since 0 is not a plausible value for the true mean difference.