### Statistical Analysis of Weight Gain Supplements: Ripped vs. GainzA dietician is conducting research on two new weight gain supplements, Ripped and Gainz, to determine if there is a significant difference in the mean weight gained (in kg) by users of each supplement. The weight gain data collected over a year from random samples is presented in the table below.#### Total Weight Gains (in kg)- **Ripped**: 12.1, 11.0, 16.3, 7.4, 11.1, 9.9, 9.4, 5.4, 11.1, 10.3, 9.5, 8.8, 8.9, 9.9- **Gainz**: 9.0, 10.5, 8.6, 8.3, 8.9, 10.5, 10.7, 10.4, 8.4, 7.6, 7.0The samples are independently drawn, and it is assumed that the weight gain data for each supplement follows a normal distribution.#### Statistical TestingTo determine if there is a statistically significant difference between the means of the two populations, a two-tailed test will be performed at a 0.05 level of significance. The hypotheses to be tested are:- **Null Hypothesis (\(H_0\))**: There is no difference in the population mean of the weights gained by people taking Ripped and Gainz.- **Alternative Hypothesis (\(H_1\))**: There is a difference in the population mean of the weights gained by people taking Ripped compared to Gainz.##### Steps for Analysis:1. **State the Hypotheses** - \(H_0\): \(\mu_{\text{Ripped}} = \mu_{\text{Gainz}}\) - \(H_1\): \(\mu_{\text{Ripped}} \neq \mu_{\text{Gainz}}\)2. **Select the Test Statistic** - Typically, a t-test is used for comparing the means of two independent samples when the population standard deviations are unknown.3. **Conduct the Test** - Input the data into statistical software or use a calculator to compute the test statistic and the p-value.4. **Make a Decision** - ### Hypothesis Testing Exercise#### Part (a): State the Hypotheses- **Null Hypothesis (H₀):** - **Alternative Hypothesis (H₁):**#### Part (b): Determine the Type of Test Statistic- **Test Statistic Type:** - Selection from a drop-down menu (options available).- **Degrees of Freedom:** #### Part (c): Find the Value of the Test Statistic- **Test Statistic Value:** - (Round to three or more decimal places.)#### Part (d): Find the p-value- **p-value:** - (Round to three or more decimal places.)#### Part (e): Conclusion at 0.05 Significance Level- **Dietician’s Conclusion:** - Question: 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? - Options: Yes / No### Instructions for Users- Use the mathematical symbols and operators provided on the right to fill in the hypotheses and other required fields.- Ensure accuracy and proper rounding as specified for statistical measures to make valid conclusions.### Additional Notes- There are tools for mathematical symbols on the right to assist in inputting the correct statistical notation.- The exercise emphasizes the key steps in hypothesis testing, involving stating hypotheses, choosing the test statistic, calculating the statistic and p-value, and interpreting results.### Resources- For more information and guidance on hypothesis testing, refer to the linked articles or educational materials provided in the platform’s resources section.

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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.) These data are shown in the table. Ripped Gainz Send data to calculator V 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? Total weight gains (in kg) 12.1, 11.0, 16.3, 7.4, 11.1, 9.6, 9.4, 5.4, 11.1, 10.3, 9.5, 8.8, 8.9, 9.9 9.0, 10.5, 8.6, 8.3, 8.9, 10.5, 10.7, 8.1, 9.1, 8.4, 7.6, 7.0 Send data to Excel 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.) Explanation (a) State the null hypothesis H. and the alternate hypothesis H₁. Ho H₁:0 (b) Determine the type of test statistic to use. Check 3 H |x X 5 a S On Р

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P