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Use technology to help you test the claim about the population mean, µ, at the given level of significance, a, using the given sample statistics. Assume the population is normally distributed. Claim: us 1200; a= 0.08; o = 207.88. Sample statistics: x = 1227.81, n=275 I'a. P1LLI.UI ..... O C. Ho: u> 1200 O D. Ho: u>1227.81 H3 us 1200 Ha: us 1227.81 OE. Ho: 21200 HH<1200 OF. Ho: H2 1227.81 Ha µ< 1227.81 Calculate the standardized test statistic. The standardizod tost ctatistic is 2.22 laces as needed.) Fail to reject o three decimal places as needed.) Reject and conclusion of the test. Ho At the 8% significance level, there V enough evidence to V the claim. View an example Get more help- Clear all Final check Help me solve this Lonyright n 2021 Pearson tducation inc. All rights reserved.I Terms of Use |Privacy Policy | PermiSSions I Contact t

Use technology to help you test the claim about the population mean, µ, at the given level of significance, a, using the given sample statistics. Assume the population is normally distributed. Claim: us 1200; a= 0.08; o = 207.88. Sample statistics: x = 1227.81, n=275 I'a. P1LLI.UI ..... O C. Ho: u> 1200 O D. Ho: u>1227.81 H3 us 1200 Ha: us 1227.81 OE. Ho: 21200 HH<1200 OF. Ho: H2 1227.81 Ha µ< 1227.81 Calculate the standardized test statistic. The standardizod tost ctatistic is 2.22 laces as needed.) Fail to reject o three decimal places as needed.) Reject and conclusion of the test. Ho At the 8% significance level, there V enough evidence to V the claim. View an example Get more help- Clear all Final check Help me solve this Lonyright n 2021 Pearson tducation inc. All rights reserved.I Terms of Use |Privacy Policy | PermiSSions I Contact t

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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# Testing a Claim About the Population Mean **Goal**: Use technology to test a claim about the population mean, with the following parameters: - Population mean (\(\mu\)): 1200 - Significance level (\(\alpha\)): 0.08 - Standard deviation (\(\sigma\)): 207.88 - Sample mean (\(\bar{x}\)): 1227.81 - Sample size (\(n\)): 275 ### Hypotheses Choose the appropriate null (\(H_0\)) and alternative hypothesis (\(H_a\)): - A) \(H_0: \mu = 1200\); \(H_a: \mu \neq 1200\) - B) \(H_0: \mu \le 1200\); \(H_a: \mu > 1200\) - C) \(H_0: \mu \ge 1200\); \(H_a: \mu < 1200\) - D) \(H_0: \mu \ge 1227.81\); \(H_a: \mu < 1227.81\) - E) \(H_0: \mu \le 1227.81\); \(H_a: \mu > 1227.81\) - F) \(H_0: \mu \ge 1227.81\); \(H_a: \mu < 1227.81\) ### Calculation Calculate the standardized test statistic: - The standardized test statistic is calculated using the formula for the z-score or t-score. The value given is 2.22. ### Decision Rule - When the standardized test statistic is calculated, decide based on the significance level whether to reject the null hypothesis. ### Conclusion Determine the conclusion of the test: - Decide whether to reject or fail to reject the null hypothesis based on the calculated statistics and the given significance level. - Use the result box to conclude: "At the 8% significance level, there is [sufficient/insufficient] evidence to [support/refute] the claim." ### Additional Resources - Tools to assist: "Help me solve this," "View an example," and "Get more help." *Copyright © 2021 Pearson Education Inc. All rights reserved.* **Note**: The absence of graphical data or diagrams allows this explanation to focus purely on textual analysis and hypothesis testing
Transcribed Image Text:# Testing a Claim About the Population Mean **Goal**: Use technology to test a claim about the population mean, with the following parameters: - Population mean (\(\mu\)): 1200 - Significance level (\(\alpha\)): 0.08 - Standard deviation (\(\sigma\)): 207.88 - Sample mean (\(\bar{x}\)): 1227.81 - Sample size (\(n\)): 275 ### Hypotheses Choose the appropriate null (\(H_0\)) and alternative hypothesis (\(H_a\)): - A) \(H_0: \mu = 1200\); \(H_a: \mu \neq 1200\) - B) \(H_0: \mu \le 1200\); \(H_a: \mu > 1200\) - C) \(H_0: \mu \ge 1200\); \(H_a: \mu < 1200\) - D) \(H_0: \mu \ge 1227.81\); \(H_a: \mu < 1227.81\) - E) \(H_0: \mu \le 1227.81\); \(H_a: \mu > 1227.81\) - F) \(H_0: \mu \ge 1227.81\); \(H_a: \mu < 1227.81\) ### Calculation Calculate the standardized test statistic: - The standardized test statistic is calculated using the formula for the z-score or t-score. The value given is 2.22. ### Decision Rule - When the standardized test statistic is calculated, decide based on the significance level whether to reject the null hypothesis. ### Conclusion Determine the conclusion of the test: - Decide whether to reject or fail to reject the null hypothesis based on the calculated statistics and the given significance level. - Use the result box to conclude: "At the 8% significance level, there is [sufficient/insufficient] evidence to [support/refute] the claim." ### Additional Resources - Tools to assist: "Help me solve this," "View an example," and "Get more help." *Copyright © 2021 Pearson Education Inc. All rights reserved.* **Note**: The absence of graphical data or diagrams allows this explanation to focus purely on textual analysis and hypothesis testing
**Hypothesis Testing for Population Mean** **Problem Statement:** Use technology to help you test the claim about the population mean, \( \mu \), at the given level of significance, \( \alpha \), using the given sample statistics. Assume the population is normally distributed. - **Claim:** \( \mu \leq 1200; \alpha = 0.08; \sigma = 207.88 \). - **Sample Statistics:** \( \bar{x} = 1227.81, n = 275 \). **Hypotheses:** - **A.** - Null Hypothesis (\( H_0 \)): \( \mu = 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu \neq 1200 \) - **B.** - Null Hypothesis (\( H_0 \)): \( \mu = 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1200 \) - **C.** - Null Hypothesis (\( H_0 \)): \( \mu \geq 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1200 \) - **D.** - Null Hypothesis (\( H_0 \)): \( \mu \leq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu > 1227.81 \) - **E.** - Null Hypothesis (\( H_0 \)): \( \mu \leq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu > 1227.81 \) - **F.** - Null Hypothesis (\( H_0 \)): \( \mu \geq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1227.81 \) **Calculation:** - Calculate the standardized test statistic. - **Standardized Test Statistic:** 2.22 (Rounded to two decimal places as needed) **P-Value:** - Determine the P-value. - **P = 0.013** (Round to three decimal places as needed) **Conclusion:** - Determine the outcome and conclusion of the test. - At
Transcribed Image Text:**Hypothesis Testing for Population Mean** **Problem Statement:** Use technology to help you test the claim about the population mean, \( \mu \), at the given level of significance, \( \alpha \), using the given sample statistics. Assume the population is normally distributed. - **Claim:** \( \mu \leq 1200; \alpha = 0.08; \sigma = 207.88 \). - **Sample Statistics:** \( \bar{x} = 1227.81, n = 275 \). **Hypotheses:** - **A.** - Null Hypothesis (\( H_0 \)): \( \mu = 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu \neq 1200 \) - **B.** - Null Hypothesis (\( H_0 \)): \( \mu = 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1200 \) - **C.** - Null Hypothesis (\( H_0 \)): \( \mu \geq 1200 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1200 \) - **D.** - Null Hypothesis (\( H_0 \)): \( \mu \leq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu > 1227.81 \) - **E.** - Null Hypothesis (\( H_0 \)): \( \mu \leq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu > 1227.81 \) - **F.** - Null Hypothesis (\( H_0 \)): \( \mu \geq 1227.81 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 1227.81 \) **Calculation:** - Calculate the standardized test statistic. - **Standardized Test Statistic:** 2.22 (Rounded to two decimal places as needed) **P-Value:** - Determine the P-value. - **P = 0.013** (Round to three decimal places as needed) **Conclusion:** - Determine the outcome and conclusion of the test. - At
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