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: $ \bar{X} $1 G = 35 months, SG² = 900 Metropolis: $ \bar{X} $M = 50 months, SM² = 1050
-Referring to Table 10-3, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.01?
A) t $\cong$ Z = -1.96
B) t $\cong$ Z = ±1.96
C) t $\cong$ Z = -2.080
D) t $\cong$ Z = -2.33

Question

Quizplus · Accepted Answer

Since the sample sizes are large (n1 = 100, n2 = 150) and the population variances are assumed to be equal, we can use the pooled t-test. The degrees of freedom for the test is df = n1 + n2 - 2 = 248. Using Table 10-3 for a two-tailed test with a level of significance of 0.01 and df = 248, we find the critical value to be approximately ±2.33. Therefore, the correct answer is D.

TABLE 10-3 a Real Estate Company Is Interested in Testing Xˉ \bar{X} Xˉ

TABLE 10-3
a Real Estate Company Is Interested in Testing $\bar{X}$