### Understanding Confidence Intervals in StatisticsThe mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 233 residents whose mean number of pounds of trash generated per person per week was 33.9 pounds, and the standard deviation was 8.2 pounds. **Round answers to 3 decimal places where possible**.**a.** To compute the confidence interval use a $\_ \_ \_) distribution.**b.** With 98% confidence the population mean number of pounds per person per week is between \(\_\_\_$ and $\_\_\_$ pounds.**c.** If many groups of 233 randomly selected members are studied, then a different confidence interval would be produced from each group. About $\_\_\_$ percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, and about $\_\_\_$ percent will not contain the true population mean number of pounds of trash generated per person per week.**Hint**: [Hints](#) **Video**: [\[+\]](#)### ExplanationThis section aims to educate on how to calculate and interpret confidence intervals in the context of statistics. The problem describes a scenario involving a study of trash generation per person in a city and outlines a step-by-step approach for deriving a 98% confidence interval.#### Breakdown of the Problem:- **Sample size (n)**: 233 residents- **Sample mean ($\bar{x}$)**: 33.9 pounds- **Standard deviation (s)**: 8.2 pounds- **Confidence level**: 98%#### Step-by-Step Solution:1. **Determine the correct distribution** for computing the confidence interval. Since the sample size is large ($n > 30$), a normal distribution or a t-distribution could be used, but the exact choice depends on whether the population standard deviation is known.2. **Calculate the confidence interval bounds**. This involves using the sample mean, standard deviation, and the critical value from the appropriate distribution at a 98% confidence level.3. **Interpret the interval**. If the same process were repeated with many different random samples: - **98% of these intervals** will contain the true population mean. - **2% of these intervals

Sample size (n) = 233Sample mean = 33.9 poundsSample standard deviation = 8.2 pounds

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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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The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 185 residents whose mean number of pounds of trash generated per person per week was 37.2 pounds and the standard deviation was 6.3 pounds. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a distribution. b. With 95% confidence the population mean number of pounds per person per week is between and pounds. c. If many groups of 185 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.
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