Question

A medical researcher says that less than 87​% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that​ country, 85​% think that healthy children should be required to be vaccinated. At alphaequals0.05​, is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below. ​

(a) Identify the claim and state Upper H 0 and Upper H Subscript a. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. Less than nothing​% of adults in the country think that healthy children should be required to be vaccinated. B. More than nothing​% of adults in the country think that healthy children should be required to be vaccinated. C. nothing​% of adults in the country think that healthy children should be required to be vaccinated. D. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not nothing​%. 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 H 0 and Upper H Subscript a. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

A. Upper H 0​: pless than nothing Upper H Subscript a​: pgreater than or equals nothing B. Upper H 0​: pnot equals nothing Upper H Subscript a​: pequals nothing C. Upper H 0​: pgreater than nothing Upper H Subscript a​: pless than or equals nothing D. Upper H 0​: pgreater than or equals nothing Upper H Subscript a​: pless than nothing E. Upper H 0​: pequals nothing Upper H Subscript a​: pnot equals nothing F. Upper H 0​: pless than or equals nothing Upper H Subscript a​: pgreater than nothing

​(b) Find the critical​ value(s) and identify the rejection​ region(s). Identify the critical​ value(s) for this test. z 0equals nothing ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.) Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to two decimal places as​ needed.) A. The rejection regions are zless than nothing and zgreater than nothing. B. The rejection region is zgreater than nothing. C. The rejection region is zless than nothing. D. The rejection region is nothingless thanzless than nothing.

​(c) Find the standardized test statistic z. zequals nothing ​(Round to two decimal places as​ needed.)

(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim. ▼ Fail to reject Reject the null hypothesis. There ▼ is is not enough evidence to ▼ support reject the​ researcher's claim. Click to select your answer(s).

Answer 1