Question

A medical researcher says that less than 84​% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 400 adults in that​ country, 81​% think that healthy children should be required to be vaccinated. At alpha=0.10​, is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below.

A. Identify the claim and state Upper H₀ and Upper H_a  Identify the claim in this scenario.

B.Let p be the population proportion of​ successes, where a success is an adult in the country who thinks that healthy children should be required to be vaccinated. State Upper H₀ and Upper H_a Select the correct choice below and fill in the answer boxes to complete your choice.

C. Find the critical​ value(s) and identify the rejection​ region(s). Identify the critical​ value(s) for this test Z_{0 .}

Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice.

D. Find the standardized test statistic z.

E. Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Answer 1

A) Claim : A medical researcher says that less than 84​% of adults in a certain country think that healthy children should be required to be vaccinated.

The hypothesis are :

H0 : P 0.84 v/s H1 : P < 0.84

B) p = probability of success = 0.81 , n = 400

c) Here the test is left tailed.

So the critical value is,

-----------( Using excel formula " =norm.s.inv( 0.10)" )

Critical region is area below -1.28. i.e. z < -1.28.

d) The test statistic is,

= -1.64

e) Here test statistic value lie in the critical region , hence we reject null hypothesis.

Conclusion :

There are sufficient evidence to conclude that less than 84​% of adults in a certain country think that healthy children should be required to be vaccinated.