Question

5. A national survey conducted in 2005 on Canadian undergraduate students with a questioner asking them whether they do part-time jobs. 1250 students participated in the survey and 802 students said they do part-time jobs. In 2020, researcher claims that there is an increase in undergraduate students doing part-time jobs due to increase in tuition fees. In January 2020, he found 963 students out of randomly selected 1420 students do part-time jobs. Do a hypothesis test at 7% significance level to test the researcher’s claim. Answer the following to do the test:

   1. State null and alternative hypotheses.

   2. State your decision rule.

   3. Calculate the test statistic.

   4. State your conclusion.

   5. Find the p-value of the test.

Answer 1

H0: p1 = p2

H1: p1 < p2

At = 0.07, the critical value is -z0.07 = -1.48

Reject H0, if z < -1.48

= 802/1250 = 0.6416

= 963/1420 = 0.6782

The pooled sample proportion (P) = ( * n1 + * n2)/(n1 + n2) = (0.6416 * 1250 + 0.6782 * 1420)/(1250 + 1420) = 0.6611

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

= sqrt(0.6611 * (1 - 0.6611) * (1/1250 + 1/1420))

= 0.0184

The test statistic is

  

  

Since the test statistic value is not less than the critical value (-0.06 > -1.48), so we should not reject the null hypothesis.

At 0.07 significance level, there is not sufficient evidence to support the researcher's claim that there is an increase in undergraduate students doing part time jobs due to increase in tuition fees.

P-value = P(Z < -0.06)

= 0.4761