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III O CONFIDENCE INTERVAL AND OTHESL... Hypothesis test for the differenc... Español A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) For the people taking Ripped, their sample mean is 10.06 with a sample variance of 6.07. For the people taking Gainz, their sample mean is 8.89 with a sample variance of 1.37. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? (a) State the null hypothesis Ho and the alternate hypothesis H₁. H₁ H₁ H₂ = 0 H₁ : ₁ - ₂ #0 (b) Determine the type of test statistic to use. 0/5 Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) Degrees of freedom: 11 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) Explanation Beatrice (e) At the 0.05 level of significance, can the dietician conclude that there is a difference between the mean weight gained by people taking Ripped and the mean weight gained by people taking Gainz? OYes No Check 2022 McGraw Hill LLC. All Rights Reserved. 1 XI ロ 0=0 OSO X a Terms of Use Privacy Center | Accessibility S □<口 Р S D

III O CONFIDENCE INTERVAL AND OTHESL... Hypothesis test for the differenc... Español A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) For the people taking Ripped, their sample mean is 10.06 with a sample variance of 6.07. For the people taking Gainz, their sample mean is 8.89 with a sample variance of 1.37. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? (a) State the null hypothesis Ho and the alternate hypothesis H₁. H₁ H₁ H₂ = 0 H₁ : ₁ - ₂ #0 (b) Determine the type of test statistic to use. 0/5 Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) Degrees of freedom: 11 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) Explanation Beatrice (e) At the 0.05 level of significance, can the dietician conclude that there is a difference between the mean weight gained by people taking Ripped and the mean weight gained by people taking Gainz? OYes No Check 2022 McGraw Hill LLC. All Rights Reserved. 1 XI ロ 0=0 OSO X a Terms of Use Privacy Center | Accessibility S □<口 Р S D

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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**Hypothesis Test for the Difference in Means** A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. **Research Details:** - The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) - For people taking Ripped: - Sample Mean: 10.06 - Sample Variance: 6.07 - For people taking Gainz: - Sample Mean: 8.89 - Sample Variance: 1.37 Assume that the two populations of weight gains are approximately normally distributed. **Objective:** Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? **Procedure:** Perform a two-tailed test. Complete the following steps. _Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)_ **Steps:** (a) State the null hypothesis \(H_0\) and the alternate hypothesis \(H_1\). - \(H_0: \mu_1 - \mu_2 = 0\) - \(H_1: \mu_1 - \mu_2 \neq 0\) (b) Determine the type of test statistic to use. - **Type:** \(t\) - **Degrees of Freedom:** 11 (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.05 level of significance, can the dietician conclude that there is a difference between the mean weight gained by people taking Ripped and the mean weight gained by people taking Gainz? - **Answer Options:** Yes / No © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility
Transcribed Image Text:**Hypothesis Test for the Difference in Means** A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. **Research Details:** - The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) - For people taking Ripped: - Sample Mean: 10.06 - Sample Variance: 6.07 - For people taking Gainz: - Sample Mean: 8.89 - Sample Variance: 1.37 Assume that the two populations of weight gains are approximately normally distributed. **Objective:** Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? **Procedure:** Perform a two-tailed test. Complete the following steps. _Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)_ **Steps:** (a) State the null hypothesis \(H_0\) and the alternate hypothesis \(H_1\). - \(H_0: \mu_1 - \mu_2 = 0\) - \(H_1: \mu_1 - \mu_2 \neq 0\) (b) Determine the type of test statistic to use. - **Type:** \(t\) - **Degrees of Freedom:** 11 (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.05 level of significance, can the dietician conclude that there is a difference between the mean weight gained by people taking Ripped and the mean weight gained by people taking Gainz? - **Answer Options:** Yes / No © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility
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