Part 3 of 6 Points: 0 of 25 Save A research center claims that at least $28 \%$ of adults in a certain country think that their taxes will be audited. In a random sample of 600 adults in that country in a recent year, $25 \%$ say they are concerned that their taxes will be audited. At $\alpha=0.10$, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. C. $\%$ of adults in the country think that their taxes will be audited. D. Less than $\%$ of adults in the country think that their taxes will be audited. Let $\mathrm{p}$ be the population proportion of successes, where a success is an adult in the country who thinks that their taxes will be audited. State $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) A. \[ \begin{array}{l} H_{0}: p> \\ H_{a}: p \leq \end{array} \] D. \[ \begin{array}{l} H_{0}: p= \\ H_{a}: p \neq \end{array} \] B. \[ \begin{array}{l} H_{0}: p \neq \\ H_{a}: p= \end{array} \] E. \[ \begin{array}{l} H_{0}: p \leq \\ H_{a}: p> \end{array} \] C. \[ \begin{array}{l} H_{0}: p< \\ H_{a}: p \geq \\ H_{0}: p \geq 0.28 \\ H_{a}: p<0.28 \end{array} \] F. (b) Find the critical value(s) and identify the rejection region(s). Identify the critical val (s) for this test. \[ \mathrm{z}_{0}=\square \] (Round to two decimal places as needed. Use a comma to separate answers as needed.) an example Get more help - Clear all Check answer

Step 1 ：State the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is the claim that the research center is making, which is that at least 28% of adults in the country think that their taxes will be audited. The alternative hypothesis is the opposite of the null hypothesis, which is that less than 28% of adults in the country think that their taxes will be audited.

Step 2 ：Find the critical value(s) and identify the rejection region(s). The critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the test statistic is more extreme in the direction of the alternative hypothesis than the critical value, the null hypothesis is rejected. The rejection region is the range of values for which the null hypothesis is not probable.

Step 3 ：Calculate the z-score using the formula and the given significance level (α=0.10). The z-score is a measure of how many standard deviations an element is from the mean. In this case, the z-score will tell us how many standard deviations 25% (the proportion of adults in the sample who think their taxes will be audited) is from 28% (the claimed proportion of adults who think their taxes will be audited).

Step 4 ：Determine the rejection region by finding the range of z-scores for which the null hypothesis would be rejected. This can be done by finding the z-score that corresponds to the given significance level (α=0.10) and determining the range of z-scores that are more extreme in the direction of the alternative hypothesis.

Step 5 ：The calculated z-score is -1.64 (rounded to two decimal places), which is less than the critical value of 1.28. This means that the test statistic is more extreme in the direction of the alternative hypothesis than the critical value, so there is enough evidence to reject the null hypothesis. The rejection region is (-∞, 1.28), which means that any z-score less than 1.28 would lead to the rejection of the null hypothesis.

Step 6 ：Final Answer: The null hypothesis is \(H_{0}: p \geq 0.28\) and the alternative hypothesis is \(H_{a}: p<0.28\). The critical value is 1.28 and the rejection region is (-∞, 1.28). Therefore, there is enough evidence to reject the center's claim. \(\boxed{H_{0}: p \geq 0.28, H_{a}: p<0.28, z = -1.64, critical\_value = 1.28, rejection\_region = (-\infty, 1.28)}\)