The test statistics that is an appropriate hypothesis test is $z =\frac{0.35 - 0.40}{\sqrt{\frac{0.35(1 - 0.35)}{60} + \frac{0.40(1 - 0.40)}{85}}}$

<h3>How to determine the test statistic</h3>

<u>40 milligrams of medication</u>

Patients = 60

Lower stress level patients = 21

The mean of this medication is:

$\bar x = \frac{x}{n}$

So, we have:

$\bar x_1 = \frac{21}{60}$

$\bar x_1 = 0.35$

<u>75 milligrams of medication</u>

Patients = 85

Lower stress level patients = 34

The mean of this medication is:

$\bar x = \frac{x}{n}$

So, we have:

$\bar x_2 = \frac{34}{85}$

$\bar x_2 =0.4$

The test statistic is then calculated as:

$z =\frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\bar x_1(1 - \bar x_1)}{n_1} + \frac{\bar x_2(1 - \bar x_2)}{n_2}}}$

The equation becomes

$z =\frac{0.35 - 0.40}{\sqrt{\frac{0.35(1 - 0.35)}{60} + \frac{0.40(1 - 0.40)}{85}}}$

Hence, the test statistics that is an appropriate hypothesis test is $z =\frac{0.35 - 0.40}{\sqrt{\frac{0.35(1 - 0.35)}{60} + \frac{0.40(1 - 0.40)}{85}}}$