Question

Statistics Class Times A professor wishes to see if students show a time preference for statistics classes. A sample of four statistics classes shows the enrollment. At =α0.01, do the students show a time preference for the classes? Use the P-value method with a TI-83 Plus/TI-84 Plus calculator. Time :800AM :1000AM :1200PM :200PM Students 22 35 29 26

Answer 1

Solution:

Statistics Class Times A professor wishes to see if students show a time preference for statistics classes.

We have to test if the students show a time preference for the classes.

Level of Significance = α = 0.01

If there is no time preference for the classes, then all frequencies must be equal.

That is expected values = N / k

We have N = 22+35+29+26 = 112

and k = 4

thus

Ei = Expected frequencies = N / k = 112 / 4 = 28

Hypothesis are:

H0: the students does not show a time preference for the classes.

Vs

H1: the students show a time preference for the classes.

Use following Steps in TI -84 Plus calculator

Press STAT and select EDIT

Under EDIT, Select L1 column and delete all old numbers and enter Oi : observed frequencies under L1

Select L2 column and delete all old numbers and enter Ei : Expected frequencies under L2

Now again press STAT button

Select TESTS

Under TESTS select X² GOF -Test

df = k - 1 = 4 - 1 = 3

L1 and L2 appears automatically for Observed and Expected

But if it is not there, then press 2ND and 1 for L1 and 2ND 2 for L2

Enter df = 3

Click on Calculate and press Enter

P-value = p = 0.3597517

P-value = 0.3598

Decision Rule:
Reject null hypothesis H0, if P-value < 0.01 level of significance, otherwise we fail to reject H0

Since P-value = 0.3598 > 0.01 level of significance, we fail to reject H0.

Conclusion:

At 0.01 level of significance, we do not have sufficient evidence to conclude that: the students show a time preference for the classes.

Thus we conclude that: the students does not show a time preference for the classes.