Questions: A research center claims that at least 32% of adults in a certain country think that their taxes will be audited. In a random sample of 1200 adults in that country in a recent year, 29% say they are concerned that their taxes will be audited. At α=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (d) below. 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 H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.)

Solution Steps

We are testing the claim made by the research center regarding the population proportion of adults who think their taxes will be audited. The hypotheses are defined as follows:

• Null Hypothesis (\(H_0\)): \(p \geq 0.32\)
• Alternative Hypothesis (\(H_a\)): \(p < 0.32\)

The test statistic for the hypothesis test is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Where:

• \(\hat{p} = 0.29\) (sample proportion)
• \(p_0 = 0.32\) (hypothesized population proportion)
• \(n = 1200\) (sample size)

Substituting the values, we find:

\[ Z = \frac{0.29 - 0.32}{\sqrt{\frac{0.32(1 - 0.32)}{1200}}} = -2.2278 \]

The P-value associated with the test statistic \(Z = -2.2278\) is calculated to be:

\[ \text{P-value} = 0.0129 \]

For a significance level of \(\alpha = 0.01\) in a left-tailed test, the critical value is:

\[ Z < -2.3263 \]

We compare the P-value to the significance level:

• Since \(0.0129 > 0.01\), we do not reject the null hypothesis.

Final Answer