Part 1 of 6 Points: 0 of 25 Save A medical researcher says that less than $81 \%$ of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, $78 \%$ think that healthy children should be required to be vaccinated. At $\alpha=0.05$, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$. 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. More than $\square \%$ of adults in the country think that healthy children should be required to be vaccinated. B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not $\square \%$. C. $\square \%$ of adults in the country think that healthy children should be required to be vaccinated. D. Less than $\square \%$ of adults in the country think that healthy children should be required to be vaccinated. Get more help . Clear all Check answer
Solution
Step 1 ：The claim in this scenario is that less than 81% of adults in the country think that healthy children should be required to be vaccinated. This is a statement made by the medical researcher and is what we are trying to test. Therefore, the correct choice is D.
Step 2 ：The null hypothesis (H0) is the statement that is being tested. In this case, it would be that 81% or more of adults in the country think that healthy children should be required to be vaccinated.
Step 3 ：The alternative hypothesis (Ha) is the statement that we will accept if the null hypothesis is rejected. In this case, it would be that less than 81% of adults in the country think that healthy children should be required to be vaccinated.
Step 4 ：So, we have: H0: p >= 0.81, Ha: p < 0.81, where p is the proportion of adults in the country who think that healthy children should be required to be vaccinated.
Step 5 ：Final Answer: \(\boxed{D. Less than 81 \% of adults in the country think that healthy children should be required to be vaccinated. H0: p >= 0.81, Ha: p < 0.81}\)
