a. Suppose you select a sample of 540 St.Paulites. Show the sampling distribution of p (to 4 decimals). E(p) = 0.33 0.0202 b. Based upon a sample of 540 St. Paulites, what is the probability that the sample proportion will be within 0.09 of the population proportion (to 4 decimals). probability = c. Suppose you select a sample of 190 St.Paulites. Show the sampling distribution of p (to 4 decimals). E(p) = Op
a. Suppose you select a sample of 540 St.Paulites. Show the sampling distribution of p (to 4 decimals). E(p) = 0.33 0.0202 b. Based upon a sample of 540 St. Paulites, what is the probability that the sample proportion will be within 0.09 of the population proportion (to 4 decimals). probability = c. Suppose you select a sample of 190 St.Paulites. Show the sampling distribution of p (to 4 decimals). E(p) = Op
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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![## Exercise: Analyzing Sample Distributions
### Background
Recent data suggests that 33% of all Americans consume bottled water more than once a week (Natural Resources Defense Council, December 4, 2015). The Natural Resources Defence Council has enlisted your help to study bottled water consumption in St. Paul. Your task is to select a sample from St. Paul to estimate the proportion of people who drink bottled water more than once weekly. It is assumed that the proportion in St. Paul mirrors the national average at 0.33.
### Tasks
#### a. Sampling Distribution for Larger Sample
- **Sample Size**: 540 St. Paulites
- **Expected Proportion (\(E(\bar{p})\))**: 0.33
- **Standard Deviation (\(\sigma_{\bar{p}}\))**: 0.0202
#### b. Probability Calculation for Larger Sample
- **Objective**: Determine the probability that the sample proportion falls within 0.09 of the population proportion.
#### c. Sampling Distribution for Smaller Sample
- **Sample Size**: 190 St. Paulites
- You need to calculate:
- **Expected Proportion (\(E(\bar{p})\))**: [Enter results]
- **Standard Deviation (\(\sigma_{\bar{p}}\))**: [Enter results]
#### d. Probability Calculation for Smaller Sample
- **Objective**: Determine the probability that the sample proportion falls within 0.09 of the population proportion based on the smaller sample size.
#### e. Precision Gain Analysis
- **Objective**: Assess the increase in precision by opting for the larger sample over the smaller one.
- **Precision Gain**: Measure by the change in probability.
### Additional Notes
- For all tasks, utilize the z-table for probability calculations.
- This exercise underlines the importance of sample size in achieving reliable statistical results.
### Feedback
- Your responses will be evaluated for correctness.
- Be sure to check your work for accuracy.
### Icon Key
- Insights on the completion status of each task will be provided through intuitive icons.
This educational activity helps reinforce the importance of sample size and its impact on precision and validity of statistical conclusions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb94e6c5-9fab-46f1-8a0b-290ffb080b99%2Fa46454ac-3459-47fc-a771-6e7dc2c81c10%2Fsd06x58_processed.png&w=3840&q=75)
Transcribed Image Text:## Exercise: Analyzing Sample Distributions
### Background
Recent data suggests that 33% of all Americans consume bottled water more than once a week (Natural Resources Defense Council, December 4, 2015). The Natural Resources Defence Council has enlisted your help to study bottled water consumption in St. Paul. Your task is to select a sample from St. Paul to estimate the proportion of people who drink bottled water more than once weekly. It is assumed that the proportion in St. Paul mirrors the national average at 0.33.
### Tasks
#### a. Sampling Distribution for Larger Sample
- **Sample Size**: 540 St. Paulites
- **Expected Proportion (\(E(\bar{p})\))**: 0.33
- **Standard Deviation (\(\sigma_{\bar{p}}\))**: 0.0202
#### b. Probability Calculation for Larger Sample
- **Objective**: Determine the probability that the sample proportion falls within 0.09 of the population proportion.
#### c. Sampling Distribution for Smaller Sample
- **Sample Size**: 190 St. Paulites
- You need to calculate:
- **Expected Proportion (\(E(\bar{p})\))**: [Enter results]
- **Standard Deviation (\(\sigma_{\bar{p}}\))**: [Enter results]
#### d. Probability Calculation for Smaller Sample
- **Objective**: Determine the probability that the sample proportion falls within 0.09 of the population proportion based on the smaller sample size.
#### e. Precision Gain Analysis
- **Objective**: Assess the increase in precision by opting for the larger sample over the smaller one.
- **Precision Gain**: Measure by the change in probability.
### Additional Notes
- For all tasks, utilize the z-table for probability calculations.
- This exercise underlines the importance of sample size in achieving reliable statistical results.
### Feedback
- Your responses will be evaluated for correctness.
- Be sure to check your work for accuracy.
### Icon Key
- Insights on the completion status of each task will be provided through intuitive icons.
This educational activity helps reinforce the importance of sample size and its impact on precision and validity of statistical conclusions.
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