Nine homes are chosen at random from real estate listings in two suburban neighborhoods, and the square footage of each home is noted in the following table. Size of Homes in Two Subdivisions
Subdivision Square Footage
Greenwood 2,710 2,837 2,322 2,818 2,304 2,771 2,366 2,595 2,812
Pinewood 2,364 2,441 2,896 2,869 2,526 2,627 2,623 2,546 3,579

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(a) Choose the appropriate hypothesis to test if there is a difference between the average sizes of homes in the two neighborhoods at the .10 significance level. Assume μ1 is the mean of home sizes in Greenwood and μ2 is the mean of home sizes in Pinewood.

H0: μ1 – μ2 = 0 vs. H1: μ1– μ2 ≠ 0
H0: μ1 – μ2 ≠ 0 vs. H1: μ1– μ2 = 0

multiple choice 1
a
b

(b) Specify the decision rule with respect to the p-value.

Reject the null hypothesis if the p-value is
less than
.10.

(c) Find the test statistic tcalc. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

tcalc

(d) Assume unequal variances to find the p-value. (Use the quick rule to determine degrees of freedom. Round your answer to 4 decimal places.)

p-value

(e) Make a decision.

We
do not reject
the null hypothesis.

(f) State your conclusion.

We
cannot
conclude that there is a difference between the sizes of homes in the two neighborhoods.