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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 statistics. Claim: p#0.21; a= 0.01; Sample statistics: p=0.14 , n= 200 Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical value(s) is/are (Round to two decimal places as needed, Use a comma to separate answers as needed.) O B. The test cannot be performed. Find the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. z= (Round to two decimal places as needed.) O B. The test cannot be performed. What is the result of the test? O A. Fail to reject Ho. The data provide sufficient evidence to support the claim. O B. Fail to reject Ho. The data do not provide sufficient evidence to support the claim. C. Reject Ho- The data do not provide sufficient evidence to support the claim. O D. Reject Ho. The data provide sufficient evidence to support the claim. The toct cannot hn norformned 46°F iQ O O O O

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 statistics. Claim: p#0.21; a= 0.01; Sample statistics: p=0.14 , n= 200 Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical value(s) is/are (Round to two decimal places as needed, Use a comma to separate answers as needed.) O B. The test cannot be performed. Find the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. z= (Round to two decimal places as needed.) O B. The test cannot be performed. What is the result of the test? O A. Fail to reject Ho. The data provide sufficient evidence to support the claim. O B. Fail to reject Ho. The data do not provide sufficient evidence to support the claim. C. Reject Ho- The data do not provide sufficient evidence to support the claim. O D. Reject Ho. The data provide sufficient evidence to support the claim. The toct cannot hn norformned 46°F iQ O O O O

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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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:** \( p \neq 0.21 \); \( \alpha = 0.01 \); Sample statistics: \( \hat{p} = 0.14 \), \( n = 200 \). **Can the normal sampling distribution be used?** - \( \circ \) A. Yes, because both \( np \) and \( nq \) are greater than or equal to 5. - \( \circ \) B. No, because \( np \) is less than 5. - \( \circ \) C. No, because \( nq \) is less than 5. - \( \circ \) D. Yes, because \( pq \) is greater than \( \alpha = 0.01 \). **State the null and alternative hypotheses.** - \( \circ \) A. \( H_0: p \leq 0.21 \) \( \quad H_a: p > 0.21 \) - \( \circ \) B. \( H_0: p \geq 0.21 \) \( \quad H_a: p < 0.21 \) - \( \circ \) C. \( H_0: p = 0.21 \) \( \quad H_a: p \neq 0.21 \) - \( \circ \) 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.** \[ \underline{\phantom{answer}} \]
Transcribed Image Text: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:** \( p \neq 0.21 \); \( \alpha = 0.01 \); Sample statistics: \( \hat{p} = 0.14 \), \( n = 200 \). **Can the normal sampling distribution be used?** - \( \circ \) A. Yes, because both \( np \) and \( nq \) are greater than or equal to 5. - \( \circ \) B. No, because \( np \) is less than 5. - \( \circ \) C. No, because \( nq \) is less than 5. - \( \circ \) D. Yes, because \( pq \) is greater than \( \alpha = 0.01 \). **State the null and alternative hypotheses.** - \( \circ \) A. \( H_0: p \leq 0.21 \) \( \quad H_a: p > 0.21 \) - \( \circ \) B. \( H_0: p \geq 0.21 \) \( \quad H_a: p < 0.21 \) - \( \circ \) C. \( H_0: p = 0.21 \) \( \quad H_a: p \neq 0.21 \) - \( \circ \) 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.** \[ \underline{\phantom{answer}} \]
**Title: Using Normal Sampling Distribution for Hypothesis Testing** **Introduction:** Explore how to determine whether the normal sampling distribution can be used for a hypothesis test, and learn to perform a test about the population proportion \( p \) at a given level of significance \( \alpha \) using sample statistics. **Example Hypothesis Test Details:** - **Claim:** \( p \neq 0.21 \) - **Level of Significance (α):** 0.01 - **Sample Statistics:** \(\hat{p} = 0.14\), \(n = 200\) **Steps for Hypothesis Testing:** 1. **Determine Critical Value(s):** - **Options:** - **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. **Find the Z-test Statistic:** - **Options:** - **A.** \( z = \) ______ (Round to two decimal places as needed.) - **B.** The test cannot be performed. 3. **Evaluate the Result of the Test:** - **Options:** - **A.** Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim. - **B.** Fail to reject \( H_0 \). The data do not 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. **Conclusion:** Use the steps above to determine the outcome of a hypothesis test regarding population proportion with the provided statistics. Accurately calculate critical values and z-test statistics, and interpret the results to make a conclusion.
Transcribed Image Text:**Title: Using Normal Sampling Distribution for Hypothesis Testing** **Introduction:** Explore how to determine whether the normal sampling distribution can be used for a hypothesis test, and learn to perform a test about the population proportion \( p \) at a given level of significance \( \alpha \) using sample statistics. **Example Hypothesis Test Details:** - **Claim:** \( p \neq 0.21 \) - **Level of Significance (α):** 0.01 - **Sample Statistics:** \(\hat{p} = 0.14\), \(n = 200\) **Steps for Hypothesis Testing:** 1. **Determine Critical Value(s):** - **Options:** - **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. **Find the Z-test Statistic:** - **Options:** - **A.** \( z = \) ______ (Round to two decimal places as needed.) - **B.** The test cannot be performed. 3. **Evaluate the Result of the Test:** - **Options:** - **A.** Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim. - **B.** Fail to reject \( H_0 \). The data do not 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. **Conclusion:** Use the steps above to determine the outcome of a hypothesis test regarding population proportion with the provided statistics. Accurately calculate critical values and z-test statistics, and interpret the results to make a conclusion.
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