Q. The MBA department is concerned that dual degree students may be receiving lower grades than the regular MBA students. Two independent random samples have been selected. 100 observations from population 1 (dual degree students) and 100 from population 2 (MBA students). The sample means obtained are X1(bar)=84 and X2(bar)=87. It is known from previous studies that the population variances are 4.0 and 5.0 respectively. Using a level of significance of .10, is there evidence that the dual degree students are receiving lower grades? Fully explain your answer.
Ans.
To Test
Ho : μ1= μ2 Vs H1 : μ1< μ2 (one tailed test)
Test Statistics: As n is large >30 so we use Normal Test
follows Standard Normal distribution N(0,1)
= -10
Putting
=84 =87 n1=100 n2=100 =4 =5 we get
P-value = P (z < -10) = 0
Since the P-value 0 < 0.1, we reject H0. It is statistically significant.
Conclusion
At the 10% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude at 0.1 level of significance that the dual degree students are receiving lower grades
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