The proportion of adverse events among healthy adults who receive the current ve

Question

The proportion of adverse events among healthy adults who receive the current version of a vaccine is 7.5 %. A new vaccine has been developed. The investigators plan to monitor 1,000 healthy volunteers who receive the new vaccine for adverse events. (We will consider these a random sample from the population.) The investigators want to know if the new vaccine has a different adverse event rate, and they ask you to plan a statistical test for them. They ask you to use a significance level of .05 as the criterion for evidence to reject the null hypothesis.

A. State the researcher’s null and alternative hypotheses.
B. Explain why the normal curve approximation may be used to find the P value.
C. What is the standard error of   under the null hypothesis?They observe 60 adverse events for their sample of 1,000 subjects.

D. Calculate the test statistic.
E. Find the P value. Give all details.
F. Using the P value you found in the previous question, state your conclusion in words. Be specific; state your conclusion in terms of the adverse event rate for the new vaccine compared to the current version.

Explanation / Answer

A. Here investigators want to know if the new vaccine has a different adverse event rate than 0.075

So H0: p=0.075 vs H1: p not equal to 0.075

B. Here n=1000 and p=0.075 so np=75>10 also nq>10 so we can use normal curve approximation

C. SE=sqrt(p(1-p)/n)=0.0083

D. Test statistics z=p=p0/SE(p0)=0.060-0.075/0.0083=-1.807

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.