A developer collects a random sample of the ages of houses from two neighborhood

Question

A developer collects a random sample of the ages of houses from two neighborhoods and finds that the summary statistics for each are as shown. Test the hypothesis that the mean age of houses in the two neighborhoods is the same. Assume that the ages of houses in each neighborhocd follow a Normal distributicn. Complete parts a through c below. Neighborhood 1 Neighborhood 2 40 35 y,-56.5 s,#772 | y,-46.4 s2 #7.89 | 5.58 a) Calculate the P-value of the statistic given that the approximation formula for degrees of freedom gives df-71.2 The P-value is (Round to four decimal places as needed.) b) Calculate the P-value of the statistic using the rule that df-min(n,-1,n2-1) The P-value is (Round to four decimal places as needed.) c) What do ou conclude at = 0.10, the null pothesisis that he mean a es o houses n the two neighborhoods are equal and the alternative hypothesis HA 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

Explanation / Answer

Solution:-

a)

D.F = 71.2

t = 5.58

p-value = less than 0.001.

b)

D.F = 35 - 1

D.F = 34

t = 5.58

p-value = less than 0.001.

c) Reject the H0. for both the cases. There is sufficient evidence to reject the claim that mean age of houses is the same in the two neighbourhoods.

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