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Clinical trials involved treating flu symptoms with a new medicine. Among 724 patients treated
with the medicine, 72 experienced a side effect of nausea. The claim is that the rate of nausea is
greater than the 6% rate experienced by flu patients given a placebo. Find a test statistic of the
proportion.

Sagot :

According to the null hypothesis, the test statistic of the proportion is of z = 120.1.

What is the null hypothesis?

The claim is that the rate of nausea is greater than the 6% rate experienced by flu patients given a placebo. At the null hypothesis, we consider the claim as false, hence the null hypothesis is:

[tex]H_0: p \leq 0.06[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

  • [tex]\overline{p}[/tex] is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

In this problem, the parameters are:

[tex]p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994[/tex]

Hence, the test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}[/tex]

[tex]z = 120.1[/tex]

You can learn more about test statistic at https://brainly.com/question/16313918

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