Chapter 10 Problem2 - QAS129:001 Instructor Dr Yudan Zheng...

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QAS129:001 Instructor: Dr. Yudan Zheng 1. A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. 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: X G = 35 months, s G 2 = 900 Metropolis: X M = 50 months, s M 2 = 1050 (1) What are the hypotheses tested by the real estate company? ANSWER: H0: ug – um >= 0 H1: ug-um < 0 (2) Which test would likely be most appropriate to employ? a. Paired t test b. Pooled-variance t test for the difference between two means c. Independent samples Z test for the difference between two means d. Related samples Z test for the mean difference ANSWER: b (3) What is the estimated standard error of the difference between the 2 sample means? ANSWER: 06 . 4 150 1 100 1 12 . 990 ) 1 1 ( 12 . 990 ) 1 150 ( ) 1 100 ( 1050 ) 1 150 ( 900 ) 1 100 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 2 1 2 2 1 2 2 2 2 1 1 2 = + × = + = - + - × - + × - = - + - - + - = n n S n n S n S
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