# MATHEMATICS

Question 5

TABLE 10-1

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

AmericanJapanese

Sample size211100

Mean SSATL Score65.7579.83

Population Std. Dev.11.076.41

Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

H0 :   A –  J   0 versus H1 :   A –  J < 0

H0 :   A –  J   0 versus H1 :   A –  J > 0

H0 :   A –  J  = 0 versus H1 :   A –  J ≠ 0

H0 : X ̅ A – X ̅  J  0 versus H1 :   X ̅  A – X ̅  J ≠ 0

Question 6

TABLE 10-5

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

StudentExam score

Before Course (1)Exam Score

After course (2)

1530670

2690770

39101000

4700710

5450550

6820870

7820770

8630610

Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

2.365

2.145

1.761

1.895

Question 7

The t test for the difference between the means of 2 independent populations assumes that the respective

sample sizes are equal.

sample variances are equal.

populations are approximately normal.

All of these.

Question 8

TABLE 10-4

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, SG2  = 900  Metropolis: X ̅M = 50 months, SM2  =1050

Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?

-8.75

-3.69

-2.33

-1.96

Question 9

TABLE 10-4

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, SG2  = 900  Metropolis: X ̅M = 50 months, SM2  =1050

Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?

4.06

5.61

8.01

16.00

Question 10

Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test.

s12  = 4      s22  = 6

n1 = 16n2 = 25

sp2 = 6.00

sp2 = 5.00

sp2 = 5.23

sp2 = 4.00

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