Question

1. The examinations in an accounting class are scaled after grading so that the mean score is 85. The professor thinks that one teaching assistant (TA) is not sufficient in teaching accounting. The professor suspects that this TA’s students have a lower mean score than other accounting students this semester. The professor draws a sample of 36 students from the TA’s class to compare with all the other accounting student’s grades. The sample returns a mean of 78. The population variance is 36. Test the professor’s claim at a 5% level of significance.

Answer 1

I) Null and alternative hypotheses

Ho : = 85

H1 : < 85

II) test statistic Z = (xbar - )/(/√n)

Z = ( 78 - 85)/(6/√36)

Test statistic Z = -7.00

III) For level of significance a = 0.05 , left tailed test

Zcritical = Z​​​​​​0.05 = -1.645

Zcritical = -1.645

IV) Decision rule : Reject the null hypothesis if Z < Zcritical , otherwise we do not reject

Our Z = -7.00 < -1.645

Conclusion : Reject the null hypothesis , There is sufficient evidence to conclude that TA’s students have a lower mean score than other accounting students this semester.