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(c) Carry out a formal test of the hypotheses suggested in part (b). Find the test statistic and P-value. (Use a = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.) P-value =

(c) Carry out a formal test of the hypotheses suggested in part (b). Find the test statistic and P-value. (Use a = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.) P-value =

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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--- ### Analyzing Caloric Content in Packaged Foods Many consumers pay close attention to nutritional information on packaged foods. Accurate labeling is crucial. A random sample of \( n = 12 \) frozen dinners of a specific type was selected, and the caloric content of each was determined. The following are the calorie values observed: 225, 244, 232, 242, 264, 265, 235, 259, 248, 225, 226, 251, 233. #### Visual Data Analysis 1. **Boxplot (Figure 1)** - Displays the distribution of calorie content values. - The range is approximately from 220 to 270 calories. - The median and quartiles are visible, indicating data spread and potential outliers. 2. **Normal Probability Plot (Figure 2)** - Plots the calorie values against a normal distribution. - The pattern is roughly linear, suggesting the data may be normally distributed. #### Statistical Hypotheses Testing **(a) Testing Hypotheses Using a t-test** - **Question:** Is it reasonable to test hypotheses about the mean calorie content \(\mu\) by using a t-test? Explain why or why not. - **Answer:** Yes, it is reasonable. The pattern in the normal probability plot is roughly linear, and since the sample was a random sample from the population, the t-test is appropriate. **(b) Stated Caloric Content and Boxplot Analysis** - **Stated Caloric Content:** 241 calories. - **Question:** Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning. - **Answer:** - No, not necessarily. It is possible that the true average content is 241, as observed differences could be due to sampling variability. 241 is inside the box of the boxplot, indicating it might not differ significantly. **(c) Formal Hypothesis Testing** - **Question:** Conduct a formal test of the hypotheses suggested in part (b) at \(\alpha = 0.05\). - **Answer:** - Conclusion based on calculations: - Reject \(H_0\): There is convincing evidence that the stated caloric content is not 241. --- This educational analysis helps understand how to verify nutritional claims using statistical methods and visual data representation.
Transcribed Image Text:--- ### Analyzing Caloric Content in Packaged Foods Many consumers pay close attention to nutritional information on packaged foods. Accurate labeling is crucial. A random sample of \( n = 12 \) frozen dinners of a specific type was selected, and the caloric content of each was determined. The following are the calorie values observed: 225, 244, 232, 242, 264, 265, 235, 259, 248, 225, 226, 251, 233. #### Visual Data Analysis 1. **Boxplot (Figure 1)** - Displays the distribution of calorie content values. - The range is approximately from 220 to 270 calories. - The median and quartiles are visible, indicating data spread and potential outliers. 2. **Normal Probability Plot (Figure 2)** - Plots the calorie values against a normal distribution. - The pattern is roughly linear, suggesting the data may be normally distributed. #### Statistical Hypotheses Testing **(a) Testing Hypotheses Using a t-test** - **Question:** Is it reasonable to test hypotheses about the mean calorie content \(\mu\) by using a t-test? Explain why or why not. - **Answer:** Yes, it is reasonable. The pattern in the normal probability plot is roughly linear, and since the sample was a random sample from the population, the t-test is appropriate. **(b) Stated Caloric Content and Boxplot Analysis** - **Stated Caloric Content:** 241 calories. - **Question:** Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning. - **Answer:** - No, not necessarily. It is possible that the true average content is 241, as observed differences could be due to sampling variability. 241 is inside the box of the boxplot, indicating it might not differ significantly. **(c) Formal Hypothesis Testing** - **Question:** Conduct a formal test of the hypotheses suggested in part (b) at \(\alpha = 0.05\). - **Answer:** - Conclusion based on calculations: - Reject \(H_0\): There is convincing evidence that the stated caloric content is not 241. --- This educational analysis helps understand how to verify nutritional claims using statistical methods and visual data representation.
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