Instruction 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { G } = 35$ months, $S _ { G } { } ^ { 2 } = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$
-Referring to Instruction 10-3,suppose $\alpha$ = 0.05.Which of the following represents the result of the relevant hypothesis test?
A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

Question

Quizplus · Accepted Answer

The null hypothesis in this scenario would state that the mean time families have been living in their current homes in Gotham is equal to or greater than in Metropolis. Given the sample means ($\bar { X } _ { G } = 35$ months for Gotham and $\bar { X } _ { M } = 50$ months for Metropolis) and assuming equal population variances, a hypothesis test (likely a two-sample t-test assuming normality and equal variances) would compare these means to test the claim. The significant difference in sample means suggests that the null hypothesis (that the mean time is equal to or greater in Gotham) would be rejected in favor of the alternative hypothesis, which posits that families in Gotham live in their homes for a shorter time than those in Metropolis, especially given a significance level of $\alpha = 0.05$.

Instruction 10-3 a Real Estate Company Is Interested in Testing XˉG=35\quad \bar { X } _ { G } = 35XˉG​=35

Instruction 10-3
a Real Estate Company Is Interested in Testing $\quad \bar { X } _ { G } = 35$