Question

In a clinical trial, 28 out of patients taking a prescription drug daily complained of fluke symptoms. Suppose is known that 2.7% of points taking competing drugs complain of tulike symptoms. Is there suficient evidence to conclude that more than 2.7% of is drugs user experience the symptoms as a side effect at the 0.1 level of significance? 5% of the population size, and the sample the requirements for testing the hypothesis Because oo (1-P) 10. the sample is Sisted (Round to one decimal place as needed) What are the nul and alterative Hypotheses? HO Ves (Type integers or decimals. Do not round) Find the best statisti, 2-(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. O A. Since P value <a, reject the null hypothesis and conclude that there is suficient evidence that more than 2.7% of the wors experience ulike symptoms. OB. Since P value <a, do not reject the null hypothesis and conclude that there is sufficient evidence that more than 2.7% of the users experience to symptoms OC. Since value, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.7% of the user experience like symptoms

Answer 1

Given : n=869 , X=28

The estimate of the sample proportion is ,

$\hat{p}=\frac{X}{n}=\frac{28}{869}=0.0322$

Because $np_0(1-p_0)=869*0.027(1-0.027)=22.8>10$ , the sample size is greater than 5% of the population size , and the sample distribution of the proportion satify the requirements for testing the hypothesis

H:p> 2.7%

The null and alternative hypothesis is ,

$H_0:p\leq 2.7\%$

H:p> 2.7%

The test is right-tailed test.

The test statistic is ,

$Z_0=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{0.0322-0.027}{\sqrt{\frac{0.027(0.027)}{869}}}=0.95$

The p-value is ,

p-value=$P(Z>|Z_{stat}|)=P(Z>0.95)=1-P(Z\leq 0.95)$

$=1-\Phi(0.95)=1-0.8289=0.1711$ ; From standard normal distribution table

Decision : Here , p-value=0.1711 > 0.01

Therefore , do not reject the null hypothesis.

Conclusion : Since , p-value>$\alpha$ , 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.