Question

a medical researcher says that less than 83% 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, 80% 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. when you know the number of successes x, the sample size n, and the population proportion p, it can be easier to use the formula shown below to find the standardized test statistic when using a z - test for a population proportion p. z = \frac{x - np}{\sqrt{npq}} (a) identify the claim and state h₀ and hₐ. 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. \square % of adults in the country think that healthy children should be required to be vaccinated. c. less than \square % of adults in the country think that healthy children should be required to be vaccinated. d. the percentage of adults in the country who think that healthy children should be required to be vaccinated is not \square %. let p be the population proportion of successes, where a success is an adult in the country who thinks that healthy

Explanation:

Step1: Analyze the Researcher's Claim

The medical researcher says "less than 83% of adults in a certain country think that healthy children should be required to be vaccinated". So we need to match this claim to the given options.

Step2: Match with Options

• Option A is about "more than", which doesn't match the researcher's claim of "less than".
• Option B is about a specific percentage (no comparison), which doesn't match the "less than" claim.
• Option C is "Less than [ ]% of adults...", and the percentage from the researcher's claim is 83, so this matches.
• Option D is about "not [ ]%", which is a two - tailed claim, not matching the one - tailed (less than) claim of the researcher.

Answer:

C. Less than 83% of adults in the country think that healthy children should be required to be vaccinated.