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. Complete parts a through c below.

​a) Find a 95% confidence interval for the mean​ difference, μ1−μ2​, in ages of houses in the two neighborhoods

b) Is 0 within the confidence interval

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

Neighborhood 1	Neighborhood 2
61	47
50	34
47	55
54	37
66	49
46	54

Answer 1

Solution-

a) 95% C.I.

b) the 0 is included in the interval (-2.55, 18.55)

c) the mean difference is in the confidence interval.

By testing our null hypothesis is true and conclusion is both means neighborhood 1 and neighborhood 2 are same.

That is houses in the different neighborhoods are built at roughly the same time.