Question

In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Latterly, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, can we conclude that the proportion passing on the first try has increased? Determine and interpret the p-value for the test.

Answer 1

H0: p <= 0.44

Ha: p > 0.44

Sample proportion $\hat{p}$ = 130 / 250 = 0.52

Test statistics

z = $\hat{p}$ - p / sqrt( p( 1 - p) / n)

= 0.52 - 0.44 / sqrt( 0.44 * 0.56 / 250)

= 2.55

This is test statistics value.

p-value = P( Z > z)

= P( Z > 2.55 )

= 1 - P( Z < 2.55)

= 1 - 0.9946

= 0.0054

Since p-value is less than 0.05 significance level, we have sufficient evidence to reject H0.

Conclusion-

We canclude that we have enough evidence to support the claim that proportion passing on the

first try has increased.