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Use technology to help you test the claim about the population mean, p, at the given level of significance, a, using the given sample statistics. Assume the population is normally distributed. Claim: us 1280; a=0.03; o = 208.94. Sample statistics: x= 1311.73, n=275 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: us 1280 H p> 1280 O B. Ho: µ> 1280 H us 1280 O C. Ho us 1311.73 O D. Ho u> 1311.73 H, us 1311.73 OΕ H μ2 1311.73 H: p< 1311.73 Ha: u> 1311.73 O E. Ho: µ21280 Ha: u< 1280 Calculate the standardized test statistic. The standardizod toct etatistic is laces as needed.) Fail to reject ree decimal places as needed.) Reject and conclusion of the test. V the claim lo. At the 3% significance level, there V enough evidence to iQ 46°F P Type here to search ort sc

Use technology to help you test the claim about the population mean, p, at the given level of significance, a, using the given sample statistics. Assume the population is normally distributed. Claim: us 1280; a=0.03; o = 208.94. Sample statistics: x= 1311.73, n=275 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: us 1280 H p> 1280 O B. Ho: µ> 1280 H us 1280 O C. Ho us 1311.73 O D. Ho u> 1311.73 H, us 1311.73 OΕ H μ2 1311.73 H: p< 1311.73 Ha: u> 1311.73 O E. Ho: µ21280 Ha: u< 1280 Calculate the standardized test statistic. The standardizod toct etatistic is laces as needed.) Fail to reject ree decimal places as needed.) Reject and conclusion of the test. V the claim lo. At the 3% significance level, there V enough evidence to iQ 46°F P Type here to search ort sc

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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**Title: Statistical Hypothesis Testing** --- **Using Technology to Test a Population Mean Claim** **Scenario:** You are given a claim to test concerning the population mean, \( \mu \), using a given level of significance and sample statistics. It is assumed that the population is normally distributed. - **Claim:** \( \mu \leq 1280 \) - **Significance Level:** \( \alpha = 0.03 \) - **Critical Value:** 208.94 - **Sample Statistics:** - Mean (\( \bar{x} \)): 1311.73 - Sample Size (\( n \)): 275 --- **Identify the Null and Alternative Hypotheses:** Choose the correct hypothesis pair from below: - **Option A:** - \( H_0: \mu \leq 1280 \) - \( H_a: \mu > 1280 \) - **Option B:** - \( H_0: \mu \geq 1280 \) - \( H_a: \mu < 1280 \) - **Option C:** - \( H_0: \mu = 1311.73 \) - \( H_a: \mu \neq 1311.73 \) - **Option D:** - \( H_0: \mu \geq 1311.73 \) - \( H_a: \mu < 1311.73 \) - **Option E:** - \( H_0: \mu \geq 1280 \) - \( H_a: \mu < 1280 \) - **Option F:** - \( H_0: \mu \leq 1311.73 \) - \( H_a: \mu < 1311.73 \) --- **Calculate the Standardized Test Statistic:** - The standardized test statistic is \( \underline{\quad} \) - (Fill in with three decimal places as needed.) --- **Decision and Conclusion:** - **Select Decision:** - Fail to reject - Reject - **Form Conclusion:** "At the 3% significance level, there is [ ] enough evidence to [ ] the claim." - **Options:** - Fail to reject / reject - Insufficient / sufficient --- Use this
Transcribed Image Text:**Title: Statistical Hypothesis Testing** --- **Using Technology to Test a Population Mean Claim** **Scenario:** You are given a claim to test concerning the population mean, \( \mu \), using a given level of significance and sample statistics. It is assumed that the population is normally distributed. - **Claim:** \( \mu \leq 1280 \) - **Significance Level:** \( \alpha = 0.03 \) - **Critical Value:** 208.94 - **Sample Statistics:** - Mean (\( \bar{x} \)): 1311.73 - Sample Size (\( n \)): 275 --- **Identify the Null and Alternative Hypotheses:** Choose the correct hypothesis pair from below: - **Option A:** - \( H_0: \mu \leq 1280 \) - \( H_a: \mu > 1280 \) - **Option B:** - \( H_0: \mu \geq 1280 \) - \( H_a: \mu < 1280 \) - **Option C:** - \( H_0: \mu = 1311.73 \) - \( H_a: \mu \neq 1311.73 \) - **Option D:** - \( H_0: \mu \geq 1311.73 \) - \( H_a: \mu < 1311.73 \) - **Option E:** - \( H_0: \mu \geq 1280 \) - \( H_a: \mu < 1280 \) - **Option F:** - \( H_0: \mu \leq 1311.73 \) - \( H_a: \mu < 1311.73 \) --- **Calculate the Standardized Test Statistic:** - The standardized test statistic is \( \underline{\quad} \) - (Fill in with three decimal places as needed.) --- **Decision and Conclusion:** - **Select Decision:** - Fail to reject - Reject - **Form Conclusion:** "At the 3% significance level, there is [ ] enough evidence to [ ] the claim." - **Options:** - Fail to reject / reject - Insufficient / sufficient --- Use this
**Title: Using Technology to Test Population Means** **Introduction:** This tutorial guides you through testing a claim about a population mean using a given level of significance, based on provided sample statistics. Assume the population is normally distributed. **Given Data:** - **Claim:** μ ≤ 1280 - **Significance Level (α):** 0.03 - **Standard Deviation (σ):** 208.94 - **Sample Statistics:** - **Mean (x̄):** 1311.73 - **Sample Size (n):** 275 **Steps to Follow:** 1. **Identify the Null and Alternative Hypotheses:** Choose the correct option for the null (H₀) and alternative (Hₐ) hypotheses: - A. H₀: μ ≤ 1280, Hₐ: μ > 1280 - B. H₀: μ ≥ 1280, Hₐ: μ < 1280 - C. H₀: μ ≤ 1311.73, Hₐ: μ > 1311.73 - D. H₀: μ ≥ 1311.73, Hₐ: μ < 1311.73 - E. H₀: μ ≥ 1280, Hₐ: μ < 1280 - F. H₀: μ ≠ 1311.73, Hₐ: μ = 1311.73 2. **Calculate the Standardized Test Statistic:** - Use the formula for the test statistic and round to two decimal places. 3. **Determine the P-value:** - Use statistical software or tables to find the p-value and round to three decimal places. 4. **Conclusion of the Test:** - Determine whether to reject or support the null hypothesis (H₀) at the 3% significance level. **Decision Statement:** - Fill in the blanks: At the 3% significance level, there [is/is not] enough evidence to [reject/support] the claim. By completing these steps, you can effectively test claims about population means using statistical methods and technology.
Transcribed Image Text:**Title: Using Technology to Test Population Means** **Introduction:** This tutorial guides you through testing a claim about a population mean using a given level of significance, based on provided sample statistics. Assume the population is normally distributed. **Given Data:** - **Claim:** μ ≤ 1280 - **Significance Level (α):** 0.03 - **Standard Deviation (σ):** 208.94 - **Sample Statistics:** - **Mean (x̄):** 1311.73 - **Sample Size (n):** 275 **Steps to Follow:** 1. **Identify the Null and Alternative Hypotheses:** Choose the correct option for the null (H₀) and alternative (Hₐ) hypotheses: - A. H₀: μ ≤ 1280, Hₐ: μ > 1280 - B. H₀: μ ≥ 1280, Hₐ: μ < 1280 - C. H₀: μ ≤ 1311.73, Hₐ: μ > 1311.73 - D. H₀: μ ≥ 1311.73, Hₐ: μ < 1311.73 - E. H₀: μ ≥ 1280, Hₐ: μ < 1280 - F. H₀: μ ≠ 1311.73, Hₐ: μ = 1311.73 2. **Calculate the Standardized Test Statistic:** - Use the formula for the test statistic and round to two decimal places. 3. **Determine the P-value:** - Use statistical software or tables to find the p-value and round to three decimal places. 4. **Conclusion of the Test:** - Determine whether to reject or support the null hypothesis (H₀) at the 3% significance level. **Decision Statement:** - Fill in the blanks: At the 3% significance level, there [is/is not] enough evidence to [reject/support] the claim. By completing these steps, you can effectively test claims about population means using statistical methods and technology.
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