Question

Question 16 4 pts A group of researchers from a medical firm are trying to understand the proportion of American adults who are allergic to a medication. In a random sample of 100 adults, 18 people say they have such an allergy. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Use 1.96 and -1.96 as the critical z-values) Ho: P=0.20 (Null) Ha: P 0.20 (Alternative Fail to reject the null hypothesis. O Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. O Cannot conclude due to lack of information. O Reject the null hypothesis.

Answer 1

We have for given example,              
Population proportion value is =0.2          
x=18          
              
n=100          
Level of significance =   0.05          
Estimate for sample proportion = 0.18          
              
Z test statistic formula for proportion
$Z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}=Z=\frac{0.18-0.2}{\sqrt{\frac{0.2(1-0.2)}{100}}}=-0.5$

P value is 0.6171............................by using Excel command =2*NORMSDIST(-0.5)

P value is 0.6171 > 0.05

Therefore we fail to reject H0.

Fail to reject the null hypothesis. O Cannot conclude due to the sample size and the population proportion not mecting the requirement needed for applying Central Limit Thearem. Cannot conclude due to lack of information Reject the null hypothesis Central Lporti O