A certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of the drug claims that more than $95 \%$ of patients taking the drug are healed within 8 weeks. In clinical trials, 210 of 220 patients suffering from acid reflux disease were healed after 8 weeks. Test the manufacturer's claim at the $\alpha=0.1$ level of significance. Because $n p_{0}\left(1-p_{0}\right)=10.5>10$, 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? $\mathrm{H}_{0}: \nabla \nabla$ versus $\mathrm{H}_{1}$ : (Type integers or decimals. Do not round.)
Solution
Step 1 ：The null hypothesis (H0) and the alternative hypothesis (H1) are statements about the population that are contradictory. The null hypothesis is usually a statement of 'no effect' or 'no difference' and is the hypothesis that the researcher tries to disprove. The alternative hypothesis is what the researcher wants to prove. In this case, the manufacturer's claim is that more than 95% of patients are healed within 8 weeks. Therefore, the null hypothesis (H0) would be that the proportion of patients healed within 8 weeks is 95% or less, and the alternative hypothesis (H1) would be that the proportion of patients healed within 8 weeks is more than 95%. So, the null and alternative hypotheses are: H0: p ≤ 0.95 H1: p > 0.95 where p is the proportion of patients healed within 8 weeks.
