Question

Approximately 19% of physics majors in the US are women. To test whether your college differs significantly from the national average, you take a random sample of 50 physics majors at your college and find that 11 are female. Calculate the appropriate test statistic to determine whether your college differs significantly from the national rate

Answer 1

Testing the hypothesis, it is found that the appropriate test statistic is z = 0.54.

At the null hypothesis, it is tested if the proportion of women physics majors in your college is the same as the national average of 19%, that is:

$H_0: p = 0.19$

At the alternative hypothesis, it is tested if the proportion is different, that is:

$H_1: p \neq 0.19$

The test statistic is given by:

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

In which:

• $\overline{p}$ is the sample proportion.
• p is the proportion tested at the null hypothesis.
• n is the sample size.

For this problem, the parameters are:

$p = 0.19, n = 50, \overline{p} = \frac{11}{50} = 0.22$

Hence, the value of the test statistic is:

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

$z = \frac{0.22 - 0.19}{\sqrt{\frac{0.19(0.81)}{50}}}$

$z = 0.54$

A similar problem is given at brainly.com/question/24166849