Question

A college administrator claims that the proportion of students that are female is greater than 62%. To test this claim, a random sample of 300 students is taken and its determined that 213 students are female. The following is the setup for this hypothesis test: {H0:p=0.62Ha:p>0.62 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Provide your answer below: $$

Answer 1

Answer: 3.21

Step-by-step explanation:

As per given description, we have

Population proportion : $p=0.62$

Sample size : n= 300

Sample proportion : $\hat{p}=\dfrac{213}{300}=0.71$

Test statistic for population proportion :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\=\dfrac{0.71-0.62}{\sqrt{\dfrac{0.62(1-0.62)}{300}}}\\\\=3.21155595947\ \ \\\\\approx3.21 \ \ \text{[Rounded to 2 decimal places. ]}$

Hence, the test statistic for this hypothesis test for a proportion= 3.21