Question

n a clinical​ trial, 18 out of 860 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.7​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.7​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.05 level of​ significance? Because np 0 left parenthesis 1 minus p 0 right parenthesisequals 14.4 greater than ​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. ​(Round to one decimal place as​ needed.) What are the null and alternative​ hypotheses? Upper H 0​: p equals 0.017 versus Upper H 1​: p greater than 0.017 ​(Type integers or decimals. Do not​ round.) Find the test​ statistic, z 0. z 0equals 0.89 ​(Round to two decimal places as​ needed.) Find the​ P-value. ​P-valueequals 0.186 ​(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 1.7​% 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 1.7​% 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 1.7​% of the users experience flulike symptoms. Your answer is correct.D. Since ​P-valueless thanalpha​, do not reject the null hypothesis and conclude that there is sufficient evidence that more than 1.7​% of the users experience flulike symptoms. please show all work

Answer 1

Ans:

Because np 0(1- p 0)= 14.4 greater than ​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.

H₀:p=0.017

H₁:p>0.017

sample proportion=18/860=0.02093

Test statistic:

z=(0.02093-0.017)/SQRT(0.017*(1-0.017)/860)

z=0.89

p-value=P(z>0.89)=0.186

correct option is:

Since ​P-value is greater than alpha​, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 1.7​% of the users experience flu like symptoms.