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: 46, 50, 56, 59, 60, 53

Neighborhood 2: 41, 50, 34, 52, 36, 57

a) Test the null hypothesis at =0.05 using the pooledt-test. Identify the null and alternative hypotheses. Choose the correct answer below.

A. H0: 12=0, HA: 12>0

B. H0: 120, HA: 12=0

C. H0: 12=0, HA: 12>0

D. H0: 12=0 HA: 120

Compute thet-statistic. Let the difference of the sample means be y1y2. (Round to three decimal places asneeded.)

t = __.

Find theP-value. (Round to four decimal places asneeded.)

The P-Value is __.

State the conclusion. Recall that =0.05.

(dropdown: Fail to reject, Reject) H0. There is (dropdown: sufficient, insufficient) evidence to reject the claim that the mean age of houses is the same in the two neighborhoods.

b) Find a 95% confidence interval using the pooled degrees of freedom. (Round to two decimal places asneeded.)

(__,__)

c) A 95% confidence interval for the mean difference in ages of houses in the two neighborhoods was (1.14,19.14). Is this result different from the result of thepooled-t confidenceinterval? Explain why or why not. Choose the correct answer below.

A. No. Since the standard deviations are fairlyclose, the two methods will result in essentially the same confidence intervals and hypothesis tests.

B. No. Since the means are fairlyclose, the two methods will result in essentially the same confidence intervals and hypothesis tests.

C. Yes. Since the standard deviations are fairlyclose, the two methods will result in essentially the same confidence intervals and hypothesis tests.

D. Yes. Since the means are fairlyclose, the two methods will result in essentially the same confidence intervals and hypothesis tests.

Please show all work, thank you!