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Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using the given sample statistic- Claim: p<0.13; a=0.10; Sample statistics: p= 0.12, n= 25 .... Can the normal sampling distribution be used? O A. Yes, because pg is greater than a= 0.10. O B. No, because np is less than 5. O C. No, because ng is less than 5. O D. Yes, because both np and nq are greater than or equal to 5. State the null and alternative hypotheses. Choose the correct answer below. O A. Ho ps0.13 H, p>0.13 O B. H, p20.13 H p<0.13 O C. Ho p=0.13 H, p#0.13 O D. The test cannot be performed. Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using the given sample statistic- Claim: p<0.13; a=0.10; Sample statistics: p= 0.12, n= 25 .... Can the normal sampling distribution be used? O A. Yes, because pg is greater than a= 0.10. O B. No, because np is less than 5. O C. No, because ng is less than 5. O D. Yes, because both np and nq are greater than or equal to 5. State the null and alternative hypotheses. Choose the correct answer below. O A. Ho ps0.13 H, p>0.13 O B. H, p20.13 H p<0.13 O C. Ho p=0.13 H, p#0.13 O D. The test cannot be performed. Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The image presents a statistical hypothesis testing problem related to a population proportion. Here's a detailed transcription suitable for an educational website: --- **Hypothesis Test for a Population Proportion** **Problem Statement:** Determine whether the normal sampling distribution can be used. If applicable, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the provided sample statistics. - **Claim:** \( p < 0.13 \) - **Level of Significance:** \( \alpha = 0.10 \) - **Sample Proportion:** \(\hat{p} = 0.12\) - **Sample Size:** \( n = 25 \) **Steps:** 1. **Identify Critical Values:** - Choose the appropriate option and complete as necessary: - **A.** The critical value(s) is/are \_\_\_\_ (Round to two decimal places as needed. Use a comma to separate answers as needed.) - **B.** The test cannot be performed. 2. **Calculate the Test Statistic:** - Find the z-test statistic. Select the correct choice below and complete as necessary: - **A.** \( z = \_\_\_\_ \) (Round to two decimal places as needed.) - **B.** The test cannot be performed. 3. **Determine the Result of the Test:** - What is the result of the test? Choose the appropriate option: - **A.** Fail to reject \( H_0 \). The data do not provide sufficient evidence to support the claim. - **B.** Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim. - **C.** Reject \( H_0 \). The data do not provide sufficient evidence to support the claim. - **D.** Reject \( H_0 \). The data provide sufficient evidence to support the claim. - **E.** The test cannot be performed. **Tools:** - Statcrunch - Calculator --- This activity guides learners through hypothesis testing for a population proportion with structured steps, from identifying critical values and calculating the test statistic to interpreting the result.
Transcribed Image Text:The image presents a statistical hypothesis testing problem related to a population proportion. Here's a detailed transcription suitable for an educational website: --- **Hypothesis Test for a Population Proportion** **Problem Statement:** Determine whether the normal sampling distribution can be used. If applicable, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the provided sample statistics. - **Claim:** \( p < 0.13 \) - **Level of Significance:** \( \alpha = 0.10 \) - **Sample Proportion:** \(\hat{p} = 0.12\) - **Sample Size:** \( n = 25 \) **Steps:** 1. **Identify Critical Values:** - Choose the appropriate option and complete as necessary: - **A.** The critical value(s) is/are \_\_\_\_ (Round to two decimal places as needed. Use a comma to separate answers as needed.) - **B.** The test cannot be performed. 2. **Calculate the Test Statistic:** - Find the z-test statistic. Select the correct choice below and complete as necessary: - **A.** \( z = \_\_\_\_ \) (Round to two decimal places as needed.) - **B.** The test cannot be performed. 3. **Determine the Result of the Test:** - What is the result of the test? Choose the appropriate option: - **A.** Fail to reject \( H_0 \). The data do not provide sufficient evidence to support the claim. - **B.** Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim. - **C.** Reject \( H_0 \). The data do not provide sufficient evidence to support the claim. - **D.** Reject \( H_0 \). The data provide sufficient evidence to support the claim. - **E.** The test cannot be performed. **Tools:** - Statcrunch - Calculator --- This activity guides learners through hypothesis testing for a population proportion with structured steps, from identifying critical values and calculating the test statistic to interpreting the result.
**Title: Understanding Normal Sampling Distribution in Hypothesis Testing** --- **Problem Statement:** Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the given sample statistics. - **Claim:** \( p < 0.13 \) - **Significance level (\( \alpha \))**: 0.10 - **Sample statistics:** - \(\hat{p} = 0.12\) - \( n = 25 \) **Question: Can the normal sampling distribution be used?** **Options:** - **A.** Yes, because \( pq \) is greater than \( \alpha = 0.10 \). - **B.** No, because \( np \) is less than 5. - **C.** No, because \( nq \) is less than 5. - **D.** Yes, because both \( np \) and \( nq \) are greater than or equal to 5. **State the Null and Alternative Hypotheses: Choose the correct answer below.** - **A.** - \( H_0: p \leq 0.13 \) - \( H_a: p > 0.13 \) - **B.** - \( H_0: p \geq 0.13 \) - \( H_a: p < 0.13 \) - **C.** - \( H_0: p = 0.13 \) - \( H_a: p \neq 0.13 \) - **D.** The test cannot be performed. **Determine the Critical Value(s):** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. **Tools:** - **Statcrunch** - **Calculator** --- *Note:* Ensure that your calculations for \( np \) and \( nq \) are based on the sample size and proportions you are testing. This is crucial in determining whether the normal approximation can be used for hypothesis testing.
Transcribed Image Text:**Title: Understanding Normal Sampling Distribution in Hypothesis Testing** --- **Problem Statement:** Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the given sample statistics. - **Claim:** \( p < 0.13 \) - **Significance level (\( \alpha \))**: 0.10 - **Sample statistics:** - \(\hat{p} = 0.12\) - \( n = 25 \) **Question: Can the normal sampling distribution be used?** **Options:** - **A.** Yes, because \( pq \) is greater than \( \alpha = 0.10 \). - **B.** No, because \( np \) is less than 5. - **C.** No, because \( nq \) is less than 5. - **D.** Yes, because both \( np \) and \( nq \) are greater than or equal to 5. **State the Null and Alternative Hypotheses: Choose the correct answer below.** - **A.** - \( H_0: p \leq 0.13 \) - \( H_a: p > 0.13 \) - **B.** - \( H_0: p \geq 0.13 \) - \( H_a: p < 0.13 \) - **C.** - \( H_0: p = 0.13 \) - \( H_a: p \neq 0.13 \) - **D.** The test cannot be performed. **Determine the Critical Value(s):** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. **Tools:** - **Statcrunch** - **Calculator** --- *Note:* Ensure that your calculations for \( np \) and \( nq \) are based on the sample size and proportions you are testing. This is crucial in determining whether the normal approximation can be used for hypothesis testing.
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