Question

Hypothesis Test: Proportion

The university lecturer also wants to ensure that not too many people fail their course (obtain a mark less than 45). They decide to test if the proportion failing their course in the new cohort is the same as in the previous cohort. In the previous cohort 6 out of 100 students failed. In the new cohort 0.269 proportion of 130 students failed.

Test your hypothesis at the 95% level, what is your p-value?

Without conducting further calculations, would a 95% confidence interval give the same conclusion? State your reasoning

Answer 1

H₀: P1 = P2

H₁: P1 P2

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                      = (0.06 * 100 + 0.269 * 130)/(100 + 130)

                                                      = 0.1781

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

    = sqrt(0.1781 * (1 - 0.1781) * (1/130 + 1/100))

    = 0.051

The test statistic z = ()/SE

                             = (0.06 - 0.269)/0.051 = -4.10

At 95% confidence level, the critical values are z^* = +/- 1.96

Since the test statistic value is less than the critical value (-4.10 < -1.96), so we should reject the null hypothesis.

So at 95% confidence level, there is not sufficient evidence to conclude that the proportion of failing their course in the new cohort is same as in the previous cohort.

P-value = 2 * P(Z < -4.10)
             = 2 * 0 = 0

The 95% confidence interval for difference in population proportions is

( +/- z^* * SE

= (0.06 - 0.269)/+/- 1.96 * 0.051

= -0.209 +/- 0.1

= -0.309, -0.109

Since the interval does not contain 0, so we should reject the null hypothesis.

so, the 95% confidence interval give the same reasoning similar as to the the hypothesis test.

   

Answer 2

Solution...

Part A:

Part B:

Yes, 95% confidence interval will also give the same conclusion...

End of the Solution...