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.

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 h₀ and hₐ. select the correct choice below and fill in the answer boxes to complete your choice.
(round to two decimal places as needed.)

a. h₀: p =
hₐ: p ≠

b. h₀: p >
hₐ: p ≤

c. h₀: p ≥
hₐ: p <

d. h₀: p ≤
hₐ: p >

e. h₀: p <
hₐ: p ≥

f. h₀: p ≠
hₐ: p =

Explanation:

Step1: Identify the claim

The researcher claims less than 72% (0.72) of adults think healthy children should be vaccinated. So the alternative hypothesis \( H_a \) should reflect this claim (\( p < 0.72 \)). The null hypothesis \( H_0 \) is the complement or the status - quo, so it should be \( p \geq 0.72 \).

Step2: Match with the options

Looking at the options, option C has \( H_0:p\geq0.72 \) and \( H_a:p < 0.72 \), which matches our identified null and alternative hypotheses.

Answer:

C. \( H_0:p\geq0.72 \)
\( H_a:p < 0.72 \)