Question

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 94​% of patients taking the drug are healed within 8 weeks. In clinical​ trials, 223 of 235 patients suffering from acid reflux disease were healed after 8 weeks. Test the​ manufacturer's claim at the alpha equals 0.05 level of significance.

Choose answers from the parenthesis when needed.

Because np 0 ( 1 minus p 0 ) equals ______ ( doesn't equal, less than, equals, greater than)  ​10, the sample size is (less than, greater than) 5% of the population​ size, and the sample ( is given to not be random, cannot be reasonably assumed to be random, can be reasonably assumed to be random, is given to be random) the requirements for testing the hypothesis ( are not , are satisfied) ​(Round to one decimal place as​ needed.)

What are the null and alternative​ hypotheses? H 0​: ( sigma, p, mu) ( greater than, less than, equals, not equals) _____ versus H 1​: ( mu, sigma, p) (greater than, equals, not equals, less than) ____ ​(Type integers or decimals. Do not​ round.)

Find the test​ statistic, z 0.

z 0 = _____ ​(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.

A. Reject the null hypothesis. There is insufficient evidence to conclude that more than 94​% of patients taking the drug are healed within 8 weeks.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that more than 94​% of patients taking the drug are healed within 8 weeks.

C. Do not reject the null hypothesis. There is sufficient evidence to conclude more than 94​% of patients taking the drug are healed within 8 weeks.

D. Reject the null hypothesis. There is sufficient evidence to conclude that more than 94​% of patients taking the drug are healed within 8 weeks.

Answer 1

because npo(1-po) =13.3 is greater than 10 , the sample size is less than or equal to 5%, of the population size, and the sample is randomly selected , the requirements for testing the hypothesis is satisfied.

null Hypothesis:               Ho:   p		=	0.940
alternate Hypothesis:    Ha: p		>	0.940

test stat z =(p̂-p)/√(p(1-p)/n)=		0.57
p value                          =		0.284

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that more than 94​% of patients taking the drug are healed within 8 weeks.