Question

Quesuun! 12 pes To 20 mi) a clinical trial, 26 out of 828 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.6% of patients taking competing rugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.6% of this drug's users experience flulike symptoms as a side effect at the = 0.01 level of significance? 5% of the population size, and the sample Because npo (1-P) - 10, the sample size is requirements for testing the hypothesis satisfied. (Round to one decimal place as needed) What are the null and alternative hypotheses? Hy versus H (Type integers or decimals. Do not round) Find the test statistic, Zo 20 - (Round to two decimal places as needed.) Find the pvalue P-value (Round to three decimal places as needed) Choose the correct conclusion below r om - le) WE to OA Since P value <a reject the null hypothesis and conclude that there is sufficient evidence that more than 20% of the users experience f B Since P.value>,reject the null hypothesis and conclude that there is not s cient evidence that more than 2.6% of the user experience C C .Since P.value , do not reject the null hypothesis and conclude that there is sufficient evidence that more than 25 of thes e de al k to select your answer and the und to

Answer 1

Given that, n = 828 and x = 26

=> sample proportion $(\hat p)$ = 26/828 = 0.0314

Population proportion (p) = 0.026 (2.6%)

Because np0(1-p0) = 21.0 > 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.

The null and alternative hypotheses are,

H0 : p = 0.026

H1 : p > 0.026

Test statistic is,

$Z = \frac {\hat p - p}{\sqrt {\frac {p*(1-p)}{n}}} = \frac { 0.0314 - 0.026}{\sqrt {\frac { 0.026*(1-0.026)}{828}}} = 0.98$

=> Z0 = 0.98

p-value = P(Z > 0.98) = 1 - P(Z < 0.98) = 1 - 0.8365 = 0.1635

=> p-value = 0.164

Conclusion : Since, p-value > $\alpha$ , do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.6% of the users experience flulike symptoms.