Question

In a clinical​ trial, 25 out of 888 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.4​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.4​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.01 level of​ significance? Because np 0 left parenthesis 1 minus p 0 right parenthesisequals nothing ▼ greater than less than equals not equals ​10, the sample size is ▼ greater than less than ​5% of the population​ size, and the sample ▼ is given to be random, is given to not be random, cannot be reasonably assumed to be random, can be reasonably assumed to be random, the requirements for testing the hypothesis ▼ are are not satisfied. ​(Round to one decimal place as​ needed.) What are the null and alternative​ hypotheses? Upper H 0​: ▼ p mu sigma ▼ less than greater than equals not equals nothing versus Upper H 1​: ▼ p sigma mu ▼ not equals equals greater than less than nothing ​(Type integers or decimals. Do not​ round.) Find the test​ statistic, z 0. z 0equals nothing ​(Round to two decimal places as​ needed.) Find the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Choose the correct conclusion below. A. Since ​P-valueless thanalpha​, reject the null hypothesis and conclude that there is sufficient evidence that more than 2.4​% of the users experience flulike symptoms. B. Since ​P-valueless thanalpha​, do not reject the null hypothesis and conclude that there is sufficient evidence that more than 2.4​% of the users experience flulike symptoms. C. Since ​P-valuegreater thanalpha​, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.4​% of the users experience flulike symptoms. D. Since ​P-valuegreater thanalpha​, reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.4​% of the users experience flulike symptoms.

Answer 1

The following information is provided:

The sample size is N = 888  

The number of favorable cases is X = 25

Sample Proportion p = 25/888 = 0.0282

Hypothesized Proportion p₀ = 0.024

In this case, n*p₀*(1-p₀) = 888*0.024*(1-0.024) = 20.80 > 10

Because np₀(1-p₀) = 20.8 greater than 10, the sample size is greater than 5% of the population​ size , and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H_o: p ≤ 0.024 versus Ha: p > 0.024

Test Statistics

The z-statistic is computed as follows:

The test​ statistic, z₀ = 0.81

The​ P-value corresponding to z₀ = 0.81 for right tailed test is 0.209 (Obtained using online P Value from Z Score Calculator. Screenshot attached)

Since p-value (0.209) greater than α (0.01), we fail to reject null hypothesis. Therefore, there is not sufficient evidence to claim that more than 2.4​% of the users experience flulike symptoms (Option C is correct).