Question

A medical school claims that more than 28% of its students plan to go into general practice. To test this claim, a random sample of 130 of the school's students is selected. Of these, 32% of them plan to go into general practice. Find the P-value for this test of the school's claim.

Answer 1

The p-value of the test is 0.1314.

Explanation:

In this case we need to test the claim made by a medical school that more than 28% of its students plan to go into general practice.

The hypothesis can be defined as follows:

H₀: The proportion of students planning to go to general practice is 28%, i.e. p = 0.28.

Hₐ: The proportion of students planning to go to general practice is more than 28%, i.e. p > 0.28.

The information provided is:

n = 130

`\hat p=0.32`

Compute the test statistic value as follows:

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

`=\frac{0.32-0.28}{\sqrt{(0.28(1-0.28))/(130)}}\\\\=1.12`

The test statistic value is 1.12.

Compute the p-value as follows:

`p-value=P(Z>1.12)\\`

`=1-P(Z<1.12)\\\\=1-0.86864\\\\=0.13136\\\\\approx 0.1314`

The p-value of the test is 0.1314.

*Use the z-table.