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confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 203 residents whose mean number of pounds of trash generated per person per week was 37.5 pounds and the standard deviation was 8.1 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 203 randomly selected members are studied, then a different confidence interval would be produced from

confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 203 residents whose mean number of pounds of trash generated per person per week was 37.5 pounds and the standard deviation was 8.1 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 203 randomly selected members are studied, then a different confidence interval would be produced from

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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### Confidence Interval Analysis for Trash Generation The 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 203 residents whose mean number of pounds of trash generated per person per week was 37.5 pounds and the standard deviation was 8.1 pounds. Round answers to three decimal places where possible. **Questions:** **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 203 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.** #### Explanation of Concepts: 1. **Mean (Average):** - The mean is the sum of all values divided by the number of values. - In this study, the mean number of pounds of trash generated per person per week is 37.5 pounds. 2. **Standard Deviation:** - The standard deviation measures the amount of variation or dispersion in a set of values. - Here, the standard deviation is 8.1 pounds. 3. **Confidence Interval:** - A confidence interval gives an estimated range of values which is likely to include the population mean. - The 98% confidence level means that if the study were repeated multiple times, 98% of the confidence intervals calculated from those studies would contain the true population mean. 4. **t-distribution:** - The t-distribution is used instead of the normal distribution when the sample size is small (typically less than 30) or when the population standard deviation is unknown. - Since the sample size here is 203, which is relatively large, the z-distribution could be used. However, the t-distribution will provide a more accurate interval since it accounts for the additional uncertainty in the estimate of the standard deviation. **Calculations:** To calculate the confidence interval, use the formula: \[ \text{Confidence Interval} = \bar{x} \pm (t_{\alpha/2} \cdot \frac{s}{\sqrt{
Transcribed Image Text:### Confidence Interval Analysis for Trash Generation The 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 203 residents whose mean number of pounds of trash generated per person per week was 37.5 pounds and the standard deviation was 8.1 pounds. Round answers to three decimal places where possible. **Questions:** **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 203 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.** #### Explanation of Concepts: 1. **Mean (Average):** - The mean is the sum of all values divided by the number of values. - In this study, the mean number of pounds of trash generated per person per week is 37.5 pounds. 2. **Standard Deviation:** - The standard deviation measures the amount of variation or dispersion in a set of values. - Here, the standard deviation is 8.1 pounds. 3. **Confidence Interval:** - A confidence interval gives an estimated range of values which is likely to include the population mean. - The 98% confidence level means that if the study were repeated multiple times, 98% of the confidence intervals calculated from those studies would contain the true population mean. 4. **t-distribution:** - The t-distribution is used instead of the normal distribution when the sample size is small (typically less than 30) or when the population standard deviation is unknown. - Since the sample size here is 203, which is relatively large, the z-distribution could be used. However, the t-distribution will provide a more accurate interval since it accounts for the additional uncertainty in the estimate of the standard deviation. **Calculations:** To calculate the confidence interval, use the formula: \[ \text{Confidence Interval} = \bar{x} \pm (t_{\alpha/2} \cdot \frac{s}{\sqrt{
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