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 18 people making inquiries at the first development is $165,000, with a standard deviation of $36,000. A corresponding sample of 28 people at the second development had a mean of $179,000, with a standard deviation of $25,000. Assume the population standard deviations are the same. At the 0.02 significance level, can Fairfield conclude that the population means are different?
State the decision rule for 0.02 significance level: H_{0}: μ_{1} = μ_{2}; H_{1}:μ_{1} ≠ μ_{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 3 decimal places.)
The statistical software output for this problem is:
Hence,
a) Degrees of freedom = n1 + n2 - 2 = 18 + 28 - 2 = 44
For 44 degrees of freedom and 0.02 significance level,
Critical t values = -2.414, 2.414
Hence,
Decision rule will be:
Reject Ho if t < -2.414 or t > 2.414
b) Test statistic = -1.558
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