Answered: 1: 7.8 6.1 6.7 8.5 9.0 10.0 9.5 2: 5.6…

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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Transcribed Image Text:**Title: Evaluating Folacin Content in Green Tea Brands** **Introduction:** Tea is the world’s most widely consumed beverage after water, yet its nutritional value remains relatively unknown. Folacin stands out as the only B vitamin present in tea in substantial amounts. With recent advancements in assay methods, accurately determining folacin content has become feasible. Below is the data on folacin content from randomly selected specimens of four leading green tea brands. **Data:** - **Brand 1:** 7.8, 6.1, 6.7, 8.5, 9.0, 10.0, 9.5 - **Brand 2:** 5.6, 7.4, 9.7, 6.0, 8.3 - **Brand 3:** 6.7, 7.4, 5.7, 5.3, 7.5, 7.3, 4.4 - **Brand 4:** 6.3, 7.2, 7.8, 4.4, 4.9, 3.9 **Research Question:** Does this data suggest that the true average folacin content is the same for all brands? **Statistical Analysis:** 1. **Hypothesis Testing:** Conduct a test using α = 0.05. State the appropriate hypotheses: - **Option A:** - Null Hypothesis (H₀): μ₁ = μ₂ = μ₃ = μ₄ - Alternative Hypothesis (Hₐ): At least two μᵢ's are unequal - **Option B:** - Null Hypothesis (H₀): μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ - Alternative Hypothesis (Hₐ): All four μᵢ's are equal - **Option C:** - Null Hypothesis (H₀): μ₁ = μ₂ = μ₃ = μ₄ - Alternative Hypothesis (Hₐ): At least two μᵢ's are unequal - **Option D:** - Null Hypothesis (H₀): μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ - Alternative Hypothesis (Hₐ

$### Statistical Analysis of Tea Blends #### State the Conclusion in the Problem Context - **Option 1**: Fail to reject $ H_0 $. There is sufficient evidence that at least two of the tea blends have different folacin content. - **Option 2**: Reject $ H_0 $. There is sufficient evidence that at least two of the tea blends have different folacin content. - **Option 3**: Reject $ H_0 $. There is not sufficient evidence that at least two of the tea blends have different folacin content. - **Option 4**: Fail to reject $ H_0 $. There is not sufficient evidence that at least two of the tea blends have different folacin content. #### Assess the Plausibility of Assumptions Required for Analysis (Select all that apply.) - The normal probability plot is linear, so the normality assumption is plausible. - The normal probability plot is S-shaped, so the normality assumption is not plausible. - The equal variance assumption is plausible because the largest standard deviation is less than twice the smallest standard deviation. - The equal variance assumption is not plausible because the largest standard deviation is more than twice the smallest standard deviation. #### Perform a Multiple Comparisons Analysis Identify significant differences among brands. (Round your answers to two decimal places.) - $ w_{12} = $ - $ w_{13} = $ - $ w_{14} = $ - $ w_{23} = $ - $ w_{24} = $ - $ w_{34} = $ **Which pairs are significantly different? (Select all that apply.)** - brand 1 and brand 2 - brand 1 and brand 3 - brand 1 and brand 4 - brand 2 and brand 3 - brand 2 and brand 4 - brand 3 and brand 4 - There are no significant differences.$

Transcribed Image Text:### Statistical Analysis of Tea Blends #### State the Conclusion in the Problem Context - **Option 1**: Fail to reject $ H_0 $. There is sufficient evidence that at least two of the tea blends have different folacin content. - **Option 2**: Reject $ H_0 $. There is sufficient evidence that at least two of the tea blends have different folacin content. - **Option 3**: Reject $ H_0 $. There is not sufficient evidence that at least two of the tea blends have different folacin content. - **Option 4**: Fail to reject $ H_0 $. There is not sufficient evidence that at least two of the tea blends have different folacin content. #### Assess the Plausibility of Assumptions Required for Analysis (Select all that apply.) - The normal probability plot is linear, so the normality assumption is plausible. - The normal probability plot is S-shaped, so the normality assumption is not plausible. - The equal variance assumption is plausible because the largest standard deviation is less than twice the smallest standard deviation. - The equal variance assumption is not plausible because the largest standard deviation is more than twice the smallest standard deviation. #### Perform a Multiple Comparisons Analysis Identify significant differences among brands. (Round your answers to two decimal places.) - $ w_{12} = $ - $ w_{13} = $ - $ w_{14} = $ - $ w_{23} = $ - $ w_{24} = $ - $ w_{34} = $ **Which pairs are significantly different? (Select all that apply.)** - brand 1 and brand 2 - brand 1 and brand 3 - brand 1 and brand 4 - brand 2 and brand 3 - brand 2 and brand 4 - brand 3 and brand 4 - There are no significant differences.

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