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.

Neighborhood 1: 56, 63, 67, 49, 65, 48

Neighborhood 2: 46, 45, 35, 48, 39, 57

a) Find a 95% confidence interval for the meandifference, 12, in ages of houses in the two neighborhoods.

(__,__) (Round to two decimal places asneeded.)

b) Is 0 within the confidenceinterval?

a) No

b) Yes

c) What does the confidence interval suggest about the null hypothesis that the mean difference is0?

A. Failtoreject H0 since 0 isnot a plausible value for the true mean difference.

B. Failtoreject H0 since 0 is a plausible value for the true mean difference.

C. Reject H0 since 0 isnot a plausible value for the true mean difference.

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

Please show all work. Thanks!