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 $\alpha$ = 0.01.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

Given the data, we would conduct a two-sample t-test to compare the means of the two populations. The question implies testing if the mean time families in Gotham live in their homes is less than in Metropolis, which suggests a one-tailed test. Without calculating the exact p-value, the significant difference in sample means (35 months for Gotham vs. 50 months for Metropolis) and the large sample sizes would likely lead to rejecting the null hypothesis (that the mean times are equal or that Gotham's mean time is greater) in favor of the alternative hypothesis (that Gotham's mean time is less), especially at a 0.01 significance level.

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 $\quad \bar { X } _ { G } = 35$