A researcher believes that average dwelling house size in one region of the country has declined in the last five years. From property records he took a random sample of fifty houses from the population (Population 1) of all houses in service this year and a random sample of fifty houses from the population (Population 2) of all houses in service five years ago, with the following results: now n1 = 50 ¯ x1 = 2392 s1 = 325 past n2 = 50 ¯ x2 = 2434 s2 = 336

The populations may be assumed to be normally distributed with equal standard deviations. Test whether the mean house size now is less than what it was five years ago, at the 10% level of significance, in the following series of steps.

Required:
a. State the null and alternative hypotheses for the test.
b. Construct the rejection region.
c. Compute the value of the test statistic, and make a decision.
d. State a conclusion about the means, based on the test you performed.