In a large public university, the number of sections of calculus to be offered i

Question

In a large public university, the number of sections of calculus to be offered in a given year depends on the proportion of students completing the prerequisite course. The mathematics department must decide how many calculus sections to create before students begin to register for classes. To help them decide, the department decides to survey a random sample of students currently enrolled in the prerequisite course. If more than 80% of these students plan to take calculus, the department will need to increase the number of sections offered. They survey 130 students, 125 of whom respond. Of these 125, 108 say they intend to take calculus in the following year.

A: On the basis of these data, would you recommend to the mathematics department that they increase the number of sections of calculus for the following year? Use appropriate statistical evidence to support your answer

B: Suppose the five missing responses from the original 130 had simply gotten lost on the department secretary's desk while the rest were being analyzed. In what way could the inclusion of these five responses have affected your recommendation?

Explanation / Answer

A) THE NULL HYPOTHESIS = Ho= p = 0.8

THE ALTERNATE HYPOTHESIS = Ha = p >0.8

the p = 108/125 = 0.864

significance level = 0.05

the critical region = 1.645

test static = (0.864 - 0.800)/sqrt(0.8*0.2/125) = 1.788

as the test static is greater then the critical region we will reject the null hypothesis

b) when we include the 5 the n = 130

test static = (0.864 - 0.800)/sqrt(0.8*0.2/130) = 1.82

again we will reject the null hypothesis

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