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,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?
A) t $\cong$
Z = -1.645
B) t$\cong$
Z = -1.96
C) t $\cong$
Z = -2.080
D) t $\cong$
Z = ± 1.96

Question

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,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?
A) t $\cong$
 Z = -1.645
B) t$\cong$
 Z = -1.96
C) t $\cong$
Z = -2.080
D) t $\cong$
 Z = ± 1.96

Quizplus · Accepted Answer

Since the sample sizes are large (greater than 30), we can use the z-distribution instead of the t-distribution. The critical value for a 2-tailed test with a level of significance of 0.05 is approximately 1.96. However, since we are testing whether the mean time in Gotham is less than the mean time in Metropolis, it is a 1-tailed test. Therefore, we need to use the negative of the critical value, which is approximately -1.645. Since the question asks for an approximation, we can use the z-value instead of the t-value. Therefore, the correct answer is A.

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