Question

a medical researcher says that less than 80% of adults in a certain country think that healthy children should be required to be vaccinated. in a random sample of 600 adults in that country, 78% think that healthy children should be required to be vaccinated. at \\( \alpha = 0.01 \\), is there enough evidence to support the researchers claim? complete parts (a) through (d) below.
(a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { 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. the percentage of adults in the country who think that healthy children should be required to be vaccinated is not \\( \\% \\).
b. more than \\( \\% \\) of adults in the country think that healthy children should be required to be vaccinated.
c. less than 80% of adults in the country think that healthy children should be required to be vaccinated.
d. \\( \\% \\) of adults in the country think that healthy children should be required to be vaccinated.
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 \\( h _ { 0 } \\) and \\( h _ { a } \\). select the correct choice below and fill in the answer boxes to complete your choice.
(round to two decimal places as needed.)
a. \\( h _ { 0 } : p \leq \\) \\( h _ { a } : p > \\)
b. \\( h _ { 0 } : p < \\) \\( h _ { a } : p \geq \\)
c. \\( h _ { 0 } : p = \\) \\( h _ { a } : p \
eq \\)
d. \\( h _ { 0 } : p > \\) \\( h _ { a } : p \leq \\)
e. \\( h _ { 0 } : p \
eq \\) \\( h _ { a } : p = \\)
f. \\( h _ { 0 } : p \geq \\) \\( h _ { a } : p < \\)

Explanation:

The claim is directly stated in the problem as "less than 80% of adults...". In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no difference, and the alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. Since the claim is about a proportion being less than a value, the null hypothesis will be the opposite (greater than or equal to) and the alternative hypothesis will be the claim (less than).

Answer:

• Claim: C. Less than \(80\%\) of adults in the country think that healthy children should be required to be vaccinated.
• Hypotheses: F. \(H_0: p\geq0.80\), \(H_a: p < 0.80\)