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. audited. b. the percentage of adults in the country who think that their taxes will be audited is not \\( \\% \\). 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 \\( 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 \\( h _ { 0 } \\) and \\( h _ { a } \\). select the correct choice below and fill in the answer boxes to complete your choice. (round to two decimal places as needed.) a. \\( h _ { 0 } : p \leq \\) \\( h _ { a } : p > \\) b. \\( h _ { 0 } : p = \\) \\( h _ { a } : p \
eq \\) c. \\( h _ { 0 } : p < \\) \\( h _ { a } : p \geq \\) d. \\( h _ { 0 } : p \
eq \\) \\( h _ { a } : p = \\) e. \\( h _ { 0 } : p \geq 0.29 \\) \\( h _ { a } : p < 0.29 \\) f. \\( h _ { 0 } : p > \\) \\( h _ { a } : p \leq \\) (b) find the critical value(s) and identify the rejection region(s). identify the critical value(s) for this test. \\( z _ { 0 } = \\) (round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Determine the type of test

Since the alternative hypothesis \(H_{a}:p < 0.29\) (left - tailed test). For a left - tailed test with significance level \(\alpha=0.10\), we look up the \(z\) - value in the standard normal distribution table.

Step2: Find the critical value

The critical value \(z_{0}\) for a left - tailed test with \(\alpha = 0.10\) is the \(z\) - value such that \(P(Z<z_{0})=\alpha\). Looking up in the standard normal table (or using a calculator with a normal distribution function, e.g., \(z=\text{NORMSINV}(0.10)\) in Excel), we get \(z_{0}=- 1.28\)

Answer:

\(-1.28\)