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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.

a) Find the value of the​ t-statistic for the​ difference, y overbar 1 minus y overbar 2
​, in sample mean ages for the null hypothesis.

 b) Calculate the degrees of freedom from the formula dfequals =  

c) Calculate the degrees of freedom using the rule that dfequals ​min(n1minus​1, n2minus ​1).

d) Find the​ P-value using the degrees of freedom from part b.

​e) Find the​ P-value using the degrees of freedom from part c.

f) What do you conclude at

alpha

equals0.05

​,

if the null hypothesis

Upper H 0

is that the mean ages of houses in the two neighborhoods are equal and the alternative hypothesis

Upper H Subscript Upper A

is that they are not​ equal?