Question

In a clinical​ trial, 26 out of 866 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 np0 (1 – p0) = ____ ____ 10, the sample size is ________ 5% of the population size, and the sample _________________ the requirements for testing the hypothesis ______ satisfied.

What are the null and alternative hypotheses?

H0: _______ versus H1: ___________

Find the test statistic, z0.

Z0 = _____ (round to two decimal places as needed)

Find the P-value.

P-value = _____ (round to three decimal places as needed)

Choose the correct conclusion below.

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.

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.

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.

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.

Answer 1

p0 = 0.027, n = 866

np0 (1 – p0) = 866 * 0.027 * (1 - 0.027) = 22.75069

Because np0 (1 – p0) = ____ >____ 10, the sample size is ___is less than_____ 5% of the population size, and the sample ____can be reasonable assumed to be random_____________ the requirements for testing the hypothesis are satisfied.

What are the null and alternative hypotheses?

H0: p0 = 0.027 versus H1: p0 > 0.027

Standard error of proportion, SE = = 0.005507815

Sample proportion, p = 26 / 866 = 0.03

Z0 = (p - p0)/SE = (0.03 - 0.027)/ 0.005507815 =  0.54

Find the P-value.

P-value = P(z > 0.54) =  0.295

alpha = 0.1

Choose the correct conclusion below.

Since ​P-value greater than alpha​, 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.