Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order

Question

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 12 people making inquiries at the first development is $145,000, with a standard deviation of $38,000. A corresponding sample of 27 people at the second development had a mean of $182,000, with a standard deviation of $32,000. Assume the population standard deviations are the same.

State the decision rule for .02 significance level: H0: 1 = 2; H1:1 2. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

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 12 people making inquiries at the first development is $145,000, with a standard deviation of $38,000. A corresponding sample of 27 people at the second development had a mean of $182,000, with a standard deviation of $32,000. Assume the population standard deviations are the same.

Explanation / Answer

1)
H0: 1 = 2; H1:1 2.

2)
s1 = 38000 , n1 = 12 , x1 = 145000 , x2 = 182000 , s2 = 32000 , n2 = 27
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(38000^2/12) + (32000^2/27)]
= 12580.1136

t = [ (x1 - x2) - d ] / SE
= [ (145000 - 182000) - 0 ] / 12580.1136
= -2.941

3)
p value is calculated using t = -2.941 , df = 37
p value = .005614.
We reject the null hypothesis.
Fairfield conclude that the population means are different

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