Fairfield Homes is developing two parcels near Pigeon Fork T

Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 13 people making inquiries at the first development is $148,000, with a standard deviation of $36,000. A corresponding sample of 24 people at the second development had a mean of $185,000, with a standard deviation of $34,000. Assume the population standard deviations are the same. 1. State the decision rule for .05 significance level: H0: 1 = 2; H1:1 2. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between -2.030 and 2.030 . 2. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic -3.04 3. At the .05 significance level, can Fairfield conclude that the population means are different? H0. Fairfield conclude that the population means are different.

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=148000
Standard Deviation(s.d1)=36000 ; Number(n1)=13
Y(Mean)=185000
Standard Deviation(s.d2)=34000; Number(n2)=24
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =148000-185000/Sqrt((1296000000/13)+(1156000000/24))
to =-3.0428
| to | =3.0428
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 12 d.f is 2.179
We got |to| = 3.04283 & | t | = 2.179
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -3.0428 ) = 0.01
Hence Value of P0.05 > 0.01,Here we Reject Ho

ANS:
H0: 1 = 2; H1:1 2
to =-3.0428
Yes, Fairfield conclude that the population means are different
Reject Ho