Question

A medical researcher says that less than 3% of adults in a certain country that healthy children should be required to be achated in a random sample of 500 adults in that county, 30% think that he children should be required to be vaccinated Al 05, is there enough evidence to support the researcher's calme Complete parte a blow th) Find the critical values and identity the rejection regions) Identify the critical values for this test (Round to two decimal places as needed. Use a comma to separate answers as needed Identify the rejection regions Select the comet choice below and in the answer boxes to complete your choice (Round to two decimal places as needed) O A The rejection regions and OB. The rejection region is 2 OC. The rejection region is OD. The rejection region is des

Answer 1

Solution:

Given

n = 500 sample size adult in a certain country.

p = 0.84 population proportion of adults think that healthy children should be required to vaccination.

q= 1- p = 0.16

$\large \hat p= 0.80$. Sample proportion of adults think that healthy children should be required to vaccination.

$\large \alpha=0.05$. Level of significance.

To test the hypothesis

Ho: p=0.84. V s Ha: p < 0.84

b) The Z critical value at $\large \alpha=0.05$ is

. From Z table

Za = 20,05 = -1.64

The Z critical value -1.64

The rejection region of the test is Z < Z critical value

Option D is correct

c) Test statistic

$\large Z= \frac{\hat p- p}{\sqrt \frac{p*(1-p)}{n}}$

$\large Z= \frac{0.80-0.84}{\sqrt \frac{0.84*0.16}{500}}$

$\large Z= \frac{0.80-0.84}{\sqrt \frac{0.1344}{500}}$

$\large Z= \frac{0.80-0.84}{\sqrt 0.0002688}$

$\large Z= \frac{-0.04}{0.0163951}$

Z= - 2.439753

Test statistic Z = - 2.44

Decision : Z < Z critical value

- 2.44 < -1.64

Reject Ho.

d) Conclusion: Reject the null hypothesis Ho there is enough evidence to support the researchers claim.