Question

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 2,729 2,603 2,572 2,484 2,633 2,455 2,812 2,790 2,443 2,717 2,304 2,796 2,774 2,535 2,628 2,325 2,580 3,395 Pinewood (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 μ 1 is the mean of home sizes in Greenwood and μ2 is the mean of home sizes in Pinewood. O a (b) Specify the decision rule with respect to the p-value Reject the null hypothesis if the p-value is less than0.10. (c) Find the test statistic (cale (A negative value should be indicated by a minus sign Round your answer to 3 decimal places.) cale (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 MacBook Pro

Answer 1

Here we have data:

Greenwood	Pinwood
2729	2717
2603	2304
2572	2796
2484	2774
2633	2535
2455	2628
2812	2325
2790	2580
2443	3395

Here calculate by excel:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	2613.444444	2672.666667
Variance	19633.77778	104441.5
Observations	9	9
Hypothesized Mean Difference	0
df	11
t Stat	-0.504386352
P(T<=t) one-tail	0.311970012
t Critical one-tail	1.363430318
P(T<=t) two-tail	0.623940023
t Critical two-tail	1.795884819

a) correct option "A"

H_o: μ1 = μ2    vs    H_a; μ1 ≠ μ2

b) Less than 0.10

c) Test statistics:

t = - 0.504

d) P-value = 2P(t> | -0.50| )

= 0.6269

e) Do not reject the null hypothesis

f) we have not sufficient evidence

( Please select in the dropdown accordingly )