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(n1minus1, 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
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?