Final answer:
To determine if there is enough evidence to support the researcher's claim, we conduct a hypothesis test comparing the sample proportion to the null hypothesis proportion. Using the given values, we find a test statistic of -2.45, which is less than the critical value at a significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the researcher's claim.
Step-by-step explanation:
To determine if there is enough evidence to support the researcher's claim that less than 85% of adults think that healthy children should be required to be vaccinated, we need to conduct a hypothesis test.
First, we state the null and alternative hypotheses:
- Null Hypothesis (H0): p = 0.85 (proportion of adults who think children should be required to be vaccinated is 85%)
- Alternative Hypothesis (H1): p < 0.85 (proportion of adults who think children should be required to be vaccinated is less than 85%)
Next, we calculate the test statistic using the sample proportion and the null hypothesis:
z = (p bar - p0) / sqrt(p0(1-p0)/n), where p bar is the sample proportion, p0 is the null hypothesis proportion, and n is the sample size.
Using the given values, we find that z = (0.83 - 0.85) / sqrt(0.85(1-0.85)/600) = -2.45.
Finally, we compare the test statistic to the critical value at a significance level of 0.05. Since the test statistic (-2.45) is less than the critical value (-1.96 for a one-tailed test), we reject the null hypothesis.
Therefore, there is enough evidence to support the researcher's claim that less than 85% of adults think that healthy children should be required to be vaccinated.