Question

Are Japanese managers more motivated than American mangers? A randomly selected group of each were administered an attitude survey, which measures motivation for upward mobility (MFUM). The survey scores are summarized below:

1. At 0.05 level of significance test if the population variances differ for Japanese and American managers.

2. Use the results in (a) and at 0.05 level of significance test if the mean for motivation for upward mobility (MFUM) score is larger for Japanese managers than the mean for American managers.

Results/Managers American Japanese Sample Mean 65.75 79.83 6.41 Sample Standard 11.07 Deviation Sample Size 211 100

Answer 1

SOLUTION

Let $\mu _{1}$ denotes the mean MFUM score for Japanese managers

and $\mu _{2}$ denotes the mean MFUM score for American managers

here we have to test

$H_{0}:\mu _{1}=\mu _{2} ~~~vs~~~H_{1}:\mu _{1}>\mu _{2}$

We can use Z-test to solve the given testing problem.

The tset statistic is

T1 T2 N 2 + n1 112

Where  $\bar{x_{1}}$ = mean of first smaple (Japanese managers) = 79.83

$\bar{x_{2}}$ = mean of second sample (American managers) = 65.75

   = standarad deviation of first sample (Japanese managers) = 6.41

= statndard deviation of second sample (American managers)= 11.07

  $n_{1}$ = size of first sample(Japanese managaers) = 100

  $n_{2}$ = size of second sample(American managers) = 211

Using the above values we get Z = 14.1391

(In Z-test for means we reject the null hypothesis if the calculated value of Z is greater than the critical value of Z for specified significance level)

From standard normal tables with 0.05 significance level the one sided critical value of Z is 1.645

Thus here the calculated value of Z (14.1391) is greater than the critical value of Z (1.645)  

Hence we reject the null hypothesis. Thus we conclude that

The average MFUM score for Japanese managers is larger than the average MFUM score for American managers.