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. 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.) $ \bigcirc $ a. $ h _ { 0 } : p \leq $ $ h _ { a } : p $ $ \bigcirc $ b. $ h _ { 0 } : p = $ $ h _ { a } : p \ eq $ $ \bigcirc $ c. $ h _ { 0 } : p $ $ \bigcirc $ b. the rejection regions are $ z $ $ \bigcirc $ c. the rejection region is $ z

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.

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.)
\$ \bigcirc \$ a. \$ h _ { 0 } : p \leq \$ \$ h _ { a } : p > \$ \$ \bigcirc \$ b. \$ h _ { 0 } : p = \$ \$ h _ { a } : p \
eq \$ \$ \bigcirc \$ c. \$ h _ { 0 } : p < \$ \$ h _ { a } : p \geq \$ \$ \bigcirc \$ d. \$ h _ { 0 } : p \
eq \$ \$ h _ { a } : p = \$ \$ \bigcirc \$ e. \$ h _ { 0 } : p \geq 0.29 \$ \$ h _ { a } : p < 0.29 \$ \$ \bigcirc \$ 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 } = - 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.)
\$ \bigcirc \$ a. the rejection region is \$ z > \$
\$ \bigcirc \$ b. the rejection regions are \$ z < \$ and \$ z > \$
\$ \bigcirc \$ c. the rejection region is \$ z < \$
\$ \bigcirc \$ d. the rejection region is \$ < z < \$

Accepted Answer

# Explanation:
## Step1: Determine the type of test
This is a one - tailed (left - tailed) hypothesis test for a proportion. The null hypothesis $H_0:p\geq0.29$ and the alternative hypothesis $H_a:p < 0.29$.
## Step2: Find the critical value
For a left - tailed test with $\alpha = 0.10$, we look up the $z$ - value in the standard normal distribution table. The critical value $z_0$ is the value such that $P(Z<z_0)=\alpha$. From the standard normal table, $z_0=- 1.28$
## Step3: Identify the rejection region
Since it is a left - tailed test ($H_a:p < 0.29$), the rejection region is $z<z_0$. Substituting $z_0=-1.28$, the rejection region is $z < - 1.28$

# Answer:
C. The rejection region is $z < - 1.28$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the type of test

Step2: Find the critical value

Step3: Identify the rejection region

Answer: