Do male and female school superintendents earn the same pay

Do male and female school superintendents earn the same pay? A sample of male and female school superintendents showed the following salaries in $’000.

At the .05 significance level, do male superintendents earn more than female superintendents?

Write the hypothesis sbtatements.

The Following Must be answered:

-->Explain what test statistic will be used and why.

-->Compute the test statistic.

-->State the decision rule and sketch it. Based on the decision rule, do you accept or reject the Null Hypothesis?

-->State your findings.   

Solution

To test H0 : population mean( male)- population mean( female) = 0 against > 0 ....

Sample n Mean StDev SE Mean( stDev / sqrt(n) )
1 15 187.0 21.0 5.422177
2 12 166.0 19.0 5.484828

Test statistic = [ sample mean(male) - sample mean( female) ] / standard error......
standard error = sqrt [ (sample variance(male) / 15 ) + ( sample variance(female) /12) ].....
   = 7.712543895....

test statistic = 21 /  7.712543895 = 2.722837015...
A 2 sample t-test statistic is choosen here because, we are here estimating population mean by sample mean and sample s.d..we don\'t have any idea about population mean and s.d.Hence, we have to use a t-test..

P-Value = 0.006
DF = 24.569... [ DF =  (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] } ]

Since, p-value is less than 0.05...
We will reject H0 and conclude than male superintendents earn more than female superintendents..