Question

In a clinical​ trial, 28 out of 878 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.7​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.7​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.1 level of​ significance? Because np 0 left parenthesis 1 minus p 0 right parenthesisequals nothing ▼ ​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, can be reasonably assumed to be random, cannot 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​: ▼ sigma p mu ▼ equals greater than less than not equals nothing versus Upper H 1​: ▼ sigma mu p ▼ less than greater than equals not equals 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-valuegreater thanalpha​, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.7​% of the users experience flulike symptoms. B. Since ​P-valuegreater thanalpha​, reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.7​% of the users experience flulike symptoms. C. Since ​P-valueless thanalpha​, reject the null hypothesis and conclude that there is sufficient evidence that more than 2.7​% of the users experience flulike symptoms. D. Since ​P-valueless thanalpha​, do not reject the null hypothesis and conclude that there is sufficient evidence that more than 2.7​% of the users experience flulike symptoms. Click to select your answer(s).

Please make it easy to read.

Answer 1

Given that

n = 878 and p = 0.027

Because np 0 left parenthesis 1 minus p 0 right parenthesisequals 23.1 > ​10, the sample size is less than ​5% of the population​ size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied

Using TI 84 calculator

STAT>TESTS>1-PropZTest

x = 28

n = 878

po = 0.027

prop > po

press ENTER

z test statistic = 0.89

p value = 0.187

p value is greater than 0.10 significance level, so we cant reject Ho

option A. Since ​P-value greater than alpha​, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.7​% of the users experience flu like symptoms