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Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.6 pounds and that the standard deviation of the weight gain was 6.9 pounds. The authors also reported that 75.7% of these students gained more than 1.3 pounds, 17.4% maintained their weight within 1.3 pounds, and 6.8% lost more than 1.3 pounds. ***Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Round your answers to three decimal places.)

Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.6 pounds and that the standard deviation of the weight gain was 6.9 pounds. The authors also reported that 75.7% of these students gained more than 1.3 pounds, 17.4% maintained their weight within 1.3 pounds, and 6.8% lost more than 1.3 pounds. ***Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Round your answers to three decimal places.)

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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Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.6 pounds and that the standard deviation of the weight gain was 6.9 pounds. The authors also reported that 75.7% of these students gained more than 1.3 pounds, 17.4% maintained their weight within 1.3 pounds, and 6.8% lost more than 1.3 pounds.
***Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Round your answers to three decimal places.)
**Title: Understanding Weight Gain Distribution and Confidence Intervals in Statistical Analysis** --- **Scenario Context:** A study examined the weight gain of 103 freshman students at a Midwestern university. The findings estimated an average weight gain of 5.6 pounds with a standard deviation of 6.9 pounds. It was noted that 75.7% of these students gained more than 1.3 pounds, 17.4% maintained their weight within 1.3 pounds, and 6.8% lost more than 1.3 pounds. **Analysis Task (a): Evaluating the Normality of the Weight Gain Distribution** - **Question:** Why might it be unreasonable to assume a normal distribution for weight gains among these students? - **Analysis:** If the weight gain distribution is approximately normal, with a sample standard deviation \(s = 6.9\) pounds and a sample mean \(\bar{x} = 5.6\) pounds, we anticipate that around 16% of observations should fall below one standard deviation from the mean. However, given the provided weight percentages, it appears unlikely due to the deviations from typical normal distribution characteristics, suggesting that the distribution may not be approximately normal. **Analysis Task (b): Justification for Using a One-Sample t Confidence Interval** - **Question:** Why is it valid to apply a one-sample t confidence interval despite potential distribution non-normality? - **Valid Reasons:** - ✔️ The sample size is at least 30, making the t-confidence interval applicable due to the Central Limit Theorem's effect. - ✔️ The sample is representative of the population under study, justifying the use of inferential methods. **Invalid/Not Applicable Reasons:** - Using statistics from a paper alone does not inherently validate the reasoning for the t confidence interval use. - Sampling specifically only from the midwestern university’s freshman does not affect the methodological justification. - The assertion regarding sample size being "at most 30" contradicts best practices for applying t confidence intervals. **Analysis Task (c): Calculating a 95% Confidence Interval** - **Question:** What is the 95% confidence interval for the population mean weight gain? (Values are rounded to three decimal places for precision). - **Results:** The confidence interval for the population mean weight gain is calculated to be between 4.267 and 6.932 pounds
Transcribed Image Text:**Title: Understanding Weight Gain Distribution and Confidence Intervals in Statistical Analysis** --- **Scenario Context:** A study examined the weight gain of 103 freshman students at a Midwestern university. The findings estimated an average weight gain of 5.6 pounds with a standard deviation of 6.9 pounds. It was noted that 75.7% of these students gained more than 1.3 pounds, 17.4% maintained their weight within 1.3 pounds, and 6.8% lost more than 1.3 pounds. **Analysis Task (a): Evaluating the Normality of the Weight Gain Distribution** - **Question:** Why might it be unreasonable to assume a normal distribution for weight gains among these students? - **Analysis:** If the weight gain distribution is approximately normal, with a sample standard deviation \(s = 6.9\) pounds and a sample mean \(\bar{x} = 5.6\) pounds, we anticipate that around 16% of observations should fall below one standard deviation from the mean. However, given the provided weight percentages, it appears unlikely due to the deviations from typical normal distribution characteristics, suggesting that the distribution may not be approximately normal. **Analysis Task (b): Justification for Using a One-Sample t Confidence Interval** - **Question:** Why is it valid to apply a one-sample t confidence interval despite potential distribution non-normality? - **Valid Reasons:** - ✔️ The sample size is at least 30, making the t-confidence interval applicable due to the Central Limit Theorem's effect. - ✔️ The sample is representative of the population under study, justifying the use of inferential methods. **Invalid/Not Applicable Reasons:** - Using statistics from a paper alone does not inherently validate the reasoning for the t confidence interval use. - Sampling specifically only from the midwestern university’s freshman does not affect the methodological justification. - The assertion regarding sample size being "at most 30" contradicts best practices for applying t confidence intervals. **Analysis Task (c): Calculating a 95% Confidence Interval** - **Question:** What is the 95% confidence interval for the population mean weight gain? (Values are rounded to three decimal places for precision). - **Results:** The confidence interval for the population mean weight gain is calculated to be between 4.267 and 6.932 pounds
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