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). Test the null hypothesis that the mean age of houses in the two neighborhoods is the same. Assume that the data come from a population that is Normally distributed. Complete parts a through f below. (3 a) Find the value of the t-statistic for the difference, {,1 2, in sample mean ages for the null hypothesis. t= |:| (Round to two decimal places as needed.) Data table Neighborhood 1 Neighborhood 2 2 NN - N 12 b) Calculate the degrees of freedom from the formula of = 2 N NN n1 n2 df = (Round to two decimal places as needed.) c) Calculate the degrees of freedom using the rule that of = min(n, - 1, n2 - 1). of = (Type a whole number.) d) Find the P-value using the degrees of freedom from part b. P = (Use the answer from part b to find this answer. Round to three decimal places as needed.) e) Find the P-value using the degrees of freedom from part c. P =_ (Use the answer from part c to find this answer. Round to three decimal places as needed.) f) What do you conclude at o = 0.10, if the null hypothesis H, is that the mean ages of houses in the two neighborhoods are equal and the alternative hypothesis HA is that they are not equal? Ho for both cases. There sufficient evidence to reject the claim that the mean age of houses is the same in the two neighborhoods