Question

a research center claims that at least 29% of adults in a certain country think that their taxes will be audited. in a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. at \\( \alpha = 0.10 \\), is there enough evidence to reject the centers claim? complete parts (a) through (d) below. (b) find the critical value(s) and identify the rejection region(s). identify the critical value(s) for this test. \\( z _ { 0 } = - 1.28 \\) (round to two decimal places as needed. use a comma to separate answers as needed.) identify the rejection region(s). select the correct choice below and fill in the answer box(es) to complete your choice. (round to two decimal places as needed.) (c) find the standardized test statistic z. \\( z = \square \\) (round to two decimal places as needed )

Explanation:

Step1: Calculate the standard error

The formula for the standard error \(SE\) of a proportion is \(SE=\sqrt{\frac{p_0(1 - p_0)}{n}}\), where \(p_0 = 0.29\) (the proportion in the null hypothesis) and \(n=800\).

$$
LATEXBLOCK0
$$

Step2: Calculate the z - statistic

The formula for the z - statistic in a proportion test is \(z=\frac{\hat{p}-p_0}{SE}\), where \(\hat{p}=0.26\) (the sample proportion) and \(p_0 = 0.29\), \(SE\approx0.016\).

$$
LATEXBLOCK1
$$

Answer:

\(z=-1.88\)