Question

In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief. Make sure to do all of the following steps: Summarize the given information, check the condition, and identify
the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

Answer 1

Answer:

The null hypothesis is  $H_0 : p \le 0.50$

The Alternative hypothesis is $H_a : p > 0.50$

The test statistics is  $Z = 0.985$

The conclusion

There is no sufficient evidence to draw the conclusion that  more than half of those that are used the drug experienced relief

Step-by-step explanation:

From the question we are told that

        The number of subjects reported experiencing significant relief from their symptoms is $x = 108$

        The sample size  is  $n = 202$

         The level of significance is  $\alpha = 0.01$

The objective of this  experiment is to know whether more than half of those who took the drug where relieved  

The null hypothesis is  $H_0 : p \le 0.50$

The Alternative hypothesis is $H_a : p > 0.50$

Where p is the population proportion.

 Generally the sample proportion. is mathematically represented as

           $\r p = \frac{x}{n}$

            $\r p = \frac{108}{202}$

            $\r p = 0.5347$

Now the test statistics is mathematically represented as

            $Z = \frac{\r p - p}{\sqrt{\frac{p(1-p)}{n} }}$

substituting values

            $Z = \frac{0.5347 - 0.50}{\sqrt{\frac{0.50(1-0.50)}{202} }}$

           $Z = 0.985$

Generally the p-value is mathematically evaluated using Excel formula as

           $p-value =1 - (NORMSDIST(Z))$

            $p-value =1 - (NORMSDIST( 0.985))$

            $p-value =1 - 0.8377$

            $p-value =0.162$

Comparing the p-value to the level of significance we see that the  p-value  is greater than the level of significance

   This means the the null hypothesis would not be rejected

Hence there is no sufficient evidence to draw the conclusion that there are more than half of those that are using the drug  experience relief