TABLE 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: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
-Referring to Table 10-3, suppose α = 0.05. Which of the following represents the correct conclusion?
A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question

TABLE 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:  G = 35 months, SG² = 900 Metropolis:  M = 50 months, SM² = 1050
-Referring to Table 10-3, suppose α = 0.05. Which of the following represents the correct conclusion?
A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. 
D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Quizplus · Accepted Answer

We need to conduct a two-sample t-test with equal variances. The null hypothesis is that the mean time families have been living in their current homes in both Gotham and Metropolis is equal, while the alternative hypothesis is that the mean time in Gotham is less than the mean time in Metropolis.

Using the information given in the table, we can calculate the pooled variance:

Sp² = ((100-1)*900 + (150-1)*1050) / (100 + 150 - 2) = 985.71

The test statistic is:

t = (35 - 50) / (sqrt(985.71)*(sqrt(1/100 + 1/150))) = -3.11

Using a t-table with 248 degrees of freedom (100+150-2), we find that the critical value for a one-tailed hypothesis test at 0.05 significance level is -1.645. Since -3.11 < -1.645, we reject the null hypothesis and conclude that there is enough evidence to support the alternative hypothesis. Therefore, the correct conclusion is B: There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.

TABLE 10-3 a Real Estate Company Is Interested in Testing Whether the Whether