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

Answer:

The p-value of the test is 0.1314.

Step-by-step 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:  

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

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

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.