A medical researcher says that less than $72 \%$ of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 500 adults in that country, $70 \%$ think that healthy children should be required to be vaccinated. At $\alpha=0.01$, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below

Step 1 ：Define the null hypothesis as the proportion of adults who think that healthy children should be required to be vaccinated is 72% or more, and the alternative hypothesis as the proportion is less than 72%.

Step 2 ：Use the sample proportion of 70% to test these hypotheses.

Step 3 ：Calculate the test statistic, which is a z-score. This measures how many standard deviations the sample proportion is away from the hypothesized proportion under the null hypothesis.

Step 4 ：Calculate the standard deviation of the sampling distribution of the sample proportion using the formula \(\sqrt{p(1-p)/n}\), where p is the hypothesized proportion and n is the sample size.

Step 5 ：Compare the test statistic to the critical value for a one-tailed test at the 0.01 significance level to decide whether to reject the null hypothesis.

Step 6 ：Given that the z-score is -0.996, which is greater than the critical value of -2.326 for a one-tailed test at the 0.01 significance level, conclude that the sample proportion of 70% is not significantly less than the hypothesized proportion of 72% at the 0.01 significance level.

Step 7 ：Conclude that there is not enough evidence to support the researcher's claim that less than 72% of adults think that healthy children should be required to be vaccinated.

Step 8 ：Final Answer: \(\boxed{\text{There is not enough evidence to support the researcher's claim at the } \alpha = 0.01 \text{ significance level.}}\)