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The data in the table to the right represent the calories and sugar (in grams) in one serving of seven different types of breakfast cereals. a. Compute and interpret the coefficient of correlation, r. b. At the 0.05 level of significance, is there a significant linear relationship between calories and sugar? (Round to three decimal places as needed.) b. Determine the hypotheses for the test. Choose the correct answer below. OA. Ho: B₁ ≤0 H₁: B₁ > 0 O D. Ho: B₁ 20 H₁: B₁ <0 Compute the test statistic. The test statistic is 3.17. (Round to two decimal places as needed.) Determine the p-value. OB. Ho: p≤0 H₁: p>0 O E. Ho: p20 H₁: p<0 Product Cereal 1 Cereal 2 Cereal 3 Cereal 4 Cereal 5 Cereal 6 Cereal 7 ⒸC. H₁: p=0 H₁: p#0 OF. Ho: Bo=0 Họ: Bo#0 The p-value is. (Round to three decimal places as needed.) Reach a decision. Reject Ho. There is sufficient evidence at the 0.05 level of significance to conclude that there is a significant linear relationship between calories and sugar. Calories 79 103 102 109 133 194 205 Sugar 5 6NWAW 12 9

The data in the table to the right represent the calories and sugar (in grams) in one serving of seven different types of breakfast cereals. a. Compute and interpret the coefficient of correlation, r. b. At the 0.05 level of significance, is there a significant linear relationship between calories and sugar? (Round to three decimal places as needed.) b. Determine the hypotheses for the test. Choose the correct answer below. OA. Ho: B₁ ≤0 H₁: B₁ > 0 O D. Ho: B₁ 20 H₁: B₁ <0 Compute the test statistic. The test statistic is 3.17. (Round to two decimal places as needed.) Determine the p-value. OB. Ho: p≤0 H₁: p>0 O E. Ho: p20 H₁: p<0 Product Cereal 1 Cereal 2 Cereal 3 Cereal 4 Cereal 5 Cereal 6 Cereal 7 ⒸC. H₁: p=0 H₁: p#0 OF. Ho: Bo=0 Họ: Bo#0 The p-value is. (Round to three decimal places as needed.) Reach a decision. Reject Ho. There is sufficient evidence at the 0.05 level of significance to conclude that there is a significant linear relationship between calories and sugar. Calories 79 103 102 109 133 194 205 Sugar 5 6NWAW 12 9

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You are testing the null hypothesis that there is no relationship between two variables, X and Y. From your sample of n = 18, you determine that SSR = 80 and SSE = 20. Complete parts (a) through (e) below. --- c. Based on your answers to (a) and (b), what statistical decision should you make? - A. Reject H₀. There is no evidence that there is a relationship between X and Y. - B. Do not reject H₀. There is evidence that there is a relationship between X and Y. - C. Do not reject H₀. There is no evidence that there is a relationship between X and Y. - D. Reject H₀. There is evidence that there is a relationship between X and Y. --- d. Compute the correlation coefficient by first computing \( r^2 \) and assuming that \( b_1 \) is negative. - \( r^2 = \) [ ] (Round to four decimal places as needed.) - \( r = \) [ ] (Round to four decimal places as needed.) --- e. At the 0.05 level of significance, is there a significant correlation between X and Y? Determine the null and alternative hypotheses for this test. - A. - H₀: ρ ≠ 0 - H₁: ρ = 0 - B. - H₀: ρ = 0 - H₁: ρ ≠ 0 - C. - H₀: ρ ≤ 0 - H₁: ρ > 0 - D. - H₀: ρ ≥ 0 - H₁: ρ < 0
Transcribed Image Text:You are testing the null hypothesis that there is no relationship between two variables, X and Y. From your sample of n = 18, you determine that SSR = 80 and SSE = 20. Complete parts (a) through (e) below. --- c. Based on your answers to (a) and (b), what statistical decision should you make? - A. Reject H₀. There is no evidence that there is a relationship between X and Y. - B. Do not reject H₀. There is evidence that there is a relationship between X and Y. - C. Do not reject H₀. There is no evidence that there is a relationship between X and Y. - D. Reject H₀. There is evidence that there is a relationship between X and Y. --- d. Compute the correlation coefficient by first computing \( r^2 \) and assuming that \( b_1 \) is negative. - \( r^2 = \) [ ] (Round to four decimal places as needed.) - \( r = \) [ ] (Round to four decimal places as needed.) --- e. At the 0.05 level of significance, is there a significant correlation between X and Y? Determine the null and alternative hypotheses for this test. - A. - H₀: ρ ≠ 0 - H₁: ρ = 0 - B. - H₀: ρ = 0 - H₁: ρ ≠ 0 - C. - H₀: ρ ≤ 0 - H₁: ρ > 0 - D. - H₀: ρ ≥ 0 - H₁: ρ < 0
The data in the table to the right represents the calories and sugar (in grams) in one serving of seven different types of breakfast cereals. **Tasks:** a. Compute and interpret the coefficient of correlation, \( r \). b. At the 0.05 level of significance, is there a significant linear relationship between calories and sugar? **Product Data:** - Cereal 1: 79 calories, 5 grams of sugar - Cereal 2: 103 calories, 1 gram of sugar - Cereal 3: 102 calories, 3 grams of sugar - Cereal 4: 109 calories, 4 grams of sugar - Cereal 5: 133 calories, 3 grams of sugar - Cereal 6: 194 calories, 12 grams of sugar - Cereal 7: 205 calories, 9 grams of sugar --- **Instructions:** (Round to three decimal places as needed.) b. Determine the hypotheses for the test. Choose the correct answer below: - A. \( H_0: \beta_1 \leq 0 \) vs. \( H_1: \beta_1 > 0 \) - B. \( H_0: \rho \leq 0 \) vs. \( H_1: \rho > 0 \) - C. \( H_0: \rho = 0 \) vs. \( H_1: \rho \neq 0 \) - D. \( H_0: \beta_1 \geq 0 \) vs. \( H_1: \beta_1 < 0 \) - E. \( H_0: \rho \geq 0 \) vs. \( H_1: \rho < 0 \) - F. \( H_0: \beta_0 = 0 \) vs. \( H_1: \beta_0 \neq 0 \) **Compute the Test Statistic:** - The test statistic is \( 3.17 \). (Round to two decimal places as needed.) **Determine the P-Value:** - The p-value is \(\_\_\). (Round to three decimal places as needed.) **Reach a Decision:** - Reject \( H_0 \). There is **sufficient** evidence at the 0.05 level of significance to conclude that there
Transcribed Image Text:The data in the table to the right represents the calories and sugar (in grams) in one serving of seven different types of breakfast cereals. **Tasks:** a. Compute and interpret the coefficient of correlation, \( r \). b. At the 0.05 level of significance, is there a significant linear relationship between calories and sugar? **Product Data:** - Cereal 1: 79 calories, 5 grams of sugar - Cereal 2: 103 calories, 1 gram of sugar - Cereal 3: 102 calories, 3 grams of sugar - Cereal 4: 109 calories, 4 grams of sugar - Cereal 5: 133 calories, 3 grams of sugar - Cereal 6: 194 calories, 12 grams of sugar - Cereal 7: 205 calories, 9 grams of sugar --- **Instructions:** (Round to three decimal places as needed.) b. Determine the hypotheses for the test. Choose the correct answer below: - A. \( H_0: \beta_1 \leq 0 \) vs. \( H_1: \beta_1 > 0 \) - B. \( H_0: \rho \leq 0 \) vs. \( H_1: \rho > 0 \) - C. \( H_0: \rho = 0 \) vs. \( H_1: \rho \neq 0 \) - D. \( H_0: \beta_1 \geq 0 \) vs. \( H_1: \beta_1 < 0 \) - E. \( H_0: \rho \geq 0 \) vs. \( H_1: \rho < 0 \) - F. \( H_0: \beta_0 = 0 \) vs. \( H_1: \beta_0 \neq 0 \) **Compute the Test Statistic:** - The test statistic is \( 3.17 \). (Round to two decimal places as needed.) **Determine the P-Value:** - The p-value is \(\_\_\). (Round to three decimal places as needed.) **Reach a Decision:** - Reject \( H_0 \). There is **sufficient** evidence at the 0.05 level of significance to conclude that there
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