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A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current home 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: ¯X _{G }= 35 months, S_{G}^{2 }= 900, ¯X_{M }= 50 months, S_{M}^{2} = 1050. Suppose that the critical values of the relevant hypothesis test at a level of significance of 0.01 is t = -2.33 and the test statistic for the difference between the sample means is t = -3.69. Which of the following represents the correct conclusion?

A. There is not enough evidence the 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 the 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 the 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 the the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis

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Answered by PhatMorr on coursehero.com

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