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 500 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.

Answer 1

Answer: It is not enough evidence to support the researcher's claim.

Step-by-step explanation:

Since we have given that

n = 500

$\hat{p}=0.85$

So, the hypothesis are as follows:

$H_0:\hat{p}<0.87\\\\H_1:\hat{p}\geq 0.87$

So, the z value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.85-0.87}{\sqrt{\dfrac{0.87\times 0.13}{500}}}\\\\z=\dfrac{-0.02}{0.015}\\\\z=-1.33$

At α = 0.05

z= -1.64

So, 1.64<-1.33

So, we accept the null hypothesis.

Hence, it is not enough evidence to support the researcher's claim.