* CORSection 8.2 Testing a Claim about a ProportionIdentify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value, state the conclusionabout the null hypothesis as well as the final conclusion about the claim1. The drug OxyCotin (oxycodone) is used to treat pain, but it is dangerous because it is additive and can be lethal.In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea. Use a 0.05significance level to test the claim that more than 20% of OxyCotin users develop nausea. Does the rate ofnausea appear to be too high?2. In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were droppedor dismissed. Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are droppedor dismissed. Should this comforting to physician?3. A random sample of 860 births in New York State included 426 boys. Use a 0.05 significance level to test theclaim that 51.2 % of newborn baby are boys. Do the result support the belief that 51.2% of newborn babies areboys?4. A Pew Research Center Poll of 1060 teens aged 13 to 17 showed that 57% of them have made new friendsonline. Use a 0.01 significance level to test the claim that half of all teens have made new friends online.< Previous2.tvAON68MacBookDD000000F80吕F3F593F4&*#$569H

According our policy we can answer only first part for remaining please repost the question. Solution : number of success , x= 52.0 sample size, n = 227 population proportion,p= 0.2 Significance level, α= 0.05 sample proportion p̂= x/n= 52.0 / 227 = 0.2291 Hypothesis test : The null and alternative hypothesis is Ho : p = 0.2 Ha : p > 0.2 Test statistic = 0.2291 - 0.2 /√( 0.2 (1- 0.2 )/ 227 = 1.1 The test statistic is 1.1 P-value : P-value =P(Z > Zobs )= P(z > 1.1 )= 0.1357 ---------- (from normal distribution z -table) ∴ P-value= 0.1357 since P-value is greater than significance level,α = 0.05 ,we failed to reject the null hypothesis Decision : fail to reject Ho Conclusion : There is not sufficient evidence to conclude that more than 20% of OxyCotin users develop nausea. The rate of nausea does not appear to be too high.