Answer to Question #196804 in Statistics and Probability for Fatine

Question

I was found that 85.6% of students at IUL worldwide are enrolling to undergraduate program. A random sample of 50 students from IUL Morocco revealed that 42 of them were enrolled in undergraduate program. Is there evidence to state that the proportion of IUL Morocco differs from the IUL Morocco proportion? Use α = 0.05

Answer 1

Below are the null and alternative Hypothesis,

Null Hypothesis, $H_0: p = 0.856$

Alternative Hypothesis, $Ha: p ≠ 0.856$

Test statistic,

$z = \dfrac{(\hat{p} - p)}{\sqrt{\frac{p(1-p)}{n}}} \\[9pt] z = \dfrac{(0.84 - 0.856)}{\sqrt{\frac{(0.856(1-0.856)}{500}}}\\[9pt] z = -1.02$

P-value Approach

P-value =P(-1.02<z<1.02)= 0.30772

As P-value >= 0.05, fail to reject null hypothesis.

There is sufficient evidence to conclude that the proportion of IUL Morocco differs from the IUL Morocco proportion.