Question

a medical researcher says that less than 72% of adults in a certain country think that healthy children should be require to be vaccinated. in a random sample of 500 adults in that country, 69% think that healthy children should be required to be vaccinated. at α = 0.05, is there enough evidence to support the researcher’s claim? complete parts (a) through (d) below.

h₀: p ≤ □ hₐ: p > □
h₀: p < □ hₐ: p ≥ □
h₀: p ≠ □ hₐ: p = □

(b) find the critical value(s) and identify the rejection region(s).
identify the critical value(s) for this test.
z₀ = □
(round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Identify Test Type

This is a left - tailed z - test for a proportion. The significance level \(\alpha = 0.05\).

Step2: Find Critical Value

For a left - tailed test with \(\alpha=0.05\), we look for the z - score such that the area to the left of it is \(0.05\). Using the standard normal distribution table (or z - table), the critical value \(z_{0}\) corresponding to an area of \(0.05\) in the left tail is approximately \(- 1.645\). Rounding to two decimal places, we get \(-1.65\).

Answer:

\(z_{0}=-1.65\)