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A new anxiety medication has been manufactured and a study is being conducted to determine whether its effectiveness depends on dose. When 40 milligrams of the medication was administered to a simple random sample (SRS) of 60 patients, 21 of them demonstrated lower stress levels. When 75 milligrams of the medication was administrated to another SRS of 85 patients, 34 of them demonstrated lower stress levels. Which of the following test statistics is an appropriate hypothesis test?

Sagot :

MrRoyal

The test statistics is used to determine if the anxiety medication can happen under a null hypothesis

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

How to determine the test statistic

40 milligrams of medication

Patients = 60

Lower stress level patients = 21

The mean of this medication is:

[tex]\bar x = \frac{x}{n}[/tex]

So, we have:

[tex]\bar x_1 = \frac{21}{60}[/tex]

[tex]\bar x_1 = 0.35[/tex]

75 milligrams of medication

Patients = 85

Lower stress level patients = 34

The mean of this medication is:

[tex]\bar x = \frac{x}{n}[/tex]

So, we have:

[tex]\bar x_2 = \frac{34}{85}[/tex]

[tex]\bar x_2 =0.4[/tex]

The test statistic is then calculated as:

[tex]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}}}[/tex]

The equation becomes

[tex]z =\frac{0.35 - 0.40}{\sqrt{\frac{0.35(1 - 0.35)}{60} + \frac{0.40(1 - 0.40)}{85}}}[/tex]

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

Read more about test statistic at:

https://brainly.com/question/15980493

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