Questions: Question 10 of 36 Statistical Tests? Indicate whether the following analysis involves a statistical test. If it does involve a statistical test, state the population parameter(s) of interest and the null and alternative hypotheses. Polling 1100 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater than 13%. No, the analysis does not involve a statistical test. Yes, the analysis does involve a statistical test. The hypotheses are H0: μ=0.13 and Ha: μ<0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: p=0.13 and Ha: p>0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: p=0.13 and Ha: p<0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: μ=0.13 and Ha: μ>0.13.

Question 10 of 36 Statistical Tests? Indicate whether the following analysis involves a statistical test. If it does involve a statistical test, state the population parameter(s) of interest and the null and alternative hypotheses. Polling 1100 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater than 13%. No, the analysis does not involve a statistical test. Yes, the analysis does involve a statistical test. The hypotheses are H0: μ=0.13 and Ha: μ<0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: p=0.13 and Ha: p>0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: p=0.13 and Ha: p<0.13. Yes, the analysis does involve a statistical test. The hypotheses are H0: μ=0.13 and Ha: μ>0.13.
Transcript text: Question 10 of 36 View Policies Current Attempt in Progress Statistical Tests? Indicate whether the following analysis involves a statistical test. If it does involve a statistical test, state the population parameter(s) of interest and the null and alternative hypotheses. Polling 1100 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater than $13 \%$. No, the analysis does not involve a statistical test. Yes, the analysis does involve a statistical test. The hypotheses are $H_{0}: \mu=0.13$ and $H_{a}: \mu<0.13$. Yes, the analysis does involve a statistical test. The hypotheses are $H_{0}: p=0.13$ and $H_{a}: p>0.13$. Yes, the analysis does involve a statistical test. The hypotheses are $H_{0}: p=0.13$ and $H_{a}: p<0.13$. Yes, the analysis does involve a statistical test. The hypotheses are $H_{0}: \mu=0.13$ and $H_{a}: \mu>0.13$. Save for Later Attempts: 0 of 3 used Submit Answer
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Solution

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Solution Steps

Step 1: Define the Hypotheses

We are testing the claim that the percentage of people in the community living in a mobile home is greater than \(13\%\). Therefore, we define the null and alternative hypotheses as follows:

  • Null Hypothesis: \(H_0: p = 0.13\)
  • Alternative Hypothesis: \(H_a: p > 0.13\)
Step 2: Calculate the Test Statistic

The test statistic for the hypothesis test for a population proportion is calculated using the formula:

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

Where:

  • \(\hat{p}\) is the sample proportion,
  • \(p_0\) is the hypothesized population proportion (0.13),
  • \(n\) is the sample size (1100).

From the output, we have:

\[ Z = 1.9724 \]

Step 3: Calculate the P-value

The P-value associated with the test statistic is given as:

\[ \text{P-value} = 0.0243 \]

Step 4: Determine the Critical Region

For a significance level of \(\alpha = 0.05\) in a one-tailed test, the critical value for \(Z\) is:

\[ Z_{\text{critical}} = 1.6449 \]

The critical region is defined as:

\[ Z > 1.6449 \]

Step 5: Make a Decision

We compare the test statistic to the critical value:

  • Since \(Z = 1.9724 > 1.6449\), we reject the null hypothesis.

Final Answer

The analysis involves a statistical test. The hypotheses are \(H_0: p = 0.13\) and \(H_a: p > 0.13\).

Thus, the answer is:

\(\boxed{\text{Yes, the analysis does involve a statistical test. The hypotheses are } H_0: p = 0.13 \text{ and } H_a: p > 0.13.}\)

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