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Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.

Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.

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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Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.

### Hypothesis Testing Example #### (c) Formal Test of Hypotheses Carry out a formal test of the hypotheses suggested in part (b). Use a significance level of \(\alpha = 0.05\). **State the appropriate null and alternative hypotheses:** - \( H_0: \mu = 241 \) - \( H_a: \mu \neq 241 \) (this option is selected) - \( H_0: \mu = 241 \) - \( H_a: \mu > 241 \) - \( H_0: \mu > 241 \) - \( H_a: \mu < 241 \) - \( H_0: \mu > 241 \) - \( H_a: \mu = 241 \) - \( H_0: \mu < 241 \) - \( H_a: \mu > 241 \) The correct hypothesis choice has a check mark. **Find the test statistic and P-value:** (Round your test statistic to one decimal place and your P-value to three decimal places.) - Test statistic: \( t = 2.201 \) (incorrect) - \( P\text{-value} = 0.05 \) (incorrect) The test statistic and P-value provided are marked as incorrect.
Transcribed Image Text:### Hypothesis Testing Example #### (c) Formal Test of Hypotheses Carry out a formal test of the hypotheses suggested in part (b). Use a significance level of \(\alpha = 0.05\). **State the appropriate null and alternative hypotheses:** - \( H_0: \mu = 241 \) - \( H_a: \mu \neq 241 \) (this option is selected) - \( H_0: \mu = 241 \) - \( H_a: \mu > 241 \) - \( H_0: \mu > 241 \) - \( H_a: \mu < 241 \) - \( H_0: \mu > 241 \) - \( H_a: \mu = 241 \) - \( H_0: \mu < 241 \) - \( H_a: \mu > 241 \) The correct hypothesis choice has a check mark. **Find the test statistic and P-value:** (Round your test statistic to one decimal place and your P-value to three decimal places.) - Test statistic: \( t = 2.201 \) (incorrect) - \( P\text{-value} = 0.05 \) (incorrect) The test statistic and P-value provided are marked as incorrect.
**Title: Understanding Caloric Content in Frozen Dinners** Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of \(n = 12\) frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot. **Calorie Observations:** - 255, 244, 239, 242, 265, 245, 259, 248, 225, 226, 251, 233 **Boxplot Explanation:** - The boxplot displays the distribution of calorie content in the sampled frozen dinners. It helps visualize the median, quartiles, and potential outliers. The central box represents the interquartile range (IQR) where the middle 50% of data lie. The lines (or "whiskers") extend to the minimum and maximum data points that are not considered outliers. **Normal Probability Plot Explanation:** - The normal probability plot compares the distribution of the sample data with a normal distribution. Each point represents a data value plotted against a normal score. If the data is normally distributed, the points will approximately follow a straight line. In this plot, most points closely align with the diagonal, indicating that the data may follow a normal distribution. **Conclusion:** - This analysis aids in verifying the accuracy of the caloric content stated on frozen dinner packages. Understanding such statistical tools is crucial for making informed purchasing decisions. **Note:** Click "Use Salt" for more information on adjusting this analysis for sodium content considerations.
Transcribed Image Text:**Title: Understanding Caloric Content in Frozen Dinners** Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of \(n = 12\) frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot. **Calorie Observations:** - 255, 244, 239, 242, 265, 245, 259, 248, 225, 226, 251, 233 **Boxplot Explanation:** - The boxplot displays the distribution of calorie content in the sampled frozen dinners. It helps visualize the median, quartiles, and potential outliers. The central box represents the interquartile range (IQR) where the middle 50% of data lie. The lines (or "whiskers") extend to the minimum and maximum data points that are not considered outliers. **Normal Probability Plot Explanation:** - The normal probability plot compares the distribution of the sample data with a normal distribution. Each point represents a data value plotted against a normal score. If the data is normally distributed, the points will approximately follow a straight line. In this plot, most points closely align with the diagonal, indicating that the data may follow a normal distribution. **Conclusion:** - This analysis aids in verifying the accuracy of the caloric content stated on frozen dinner packages. Understanding such statistical tools is crucial for making informed purchasing decisions. **Note:** Click "Use Salt" for more information on adjusting this analysis for sodium content considerations.
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