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Determine U-x and ox from the given parameters of the population and sample size.. A = 81 0=18 n = 36

Determine U-x and ox from the given parameters of the population and sample size.. A = 81 0=18 n = 36

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 8PPS
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### Determining Population and Sample Statistics #### Problem Statement: Determine \(\mu_{\bar{x}}\) and \(\sigma_{\bar{x}}\) from the given parameters of the population and sample size. Given Data: - Population Mean (\(\mu\)): 81 - Population Standard Deviation (\(\sigma\)): 18 - Sample Size (\(n\)): 36 #### Explanation: To solve this problem, we need to calculate the sample mean (\(\mu_{\bar{x}}\)) and the sample standard deviation (\(\sigma_{\bar{x}}\)) using the given population parameters. In sampling distribution theory, the sample mean and standard deviation for the sample mean are calculated as follows: 1. **Sample Mean (\(\mu_{\bar{x}}\))**: - The sample mean is equal to the population mean. - \(\mu_{\bar{x}} = \mu\) - Thus, \(\mu_{\bar{x}} = 81\). 2. **Sample Standard Deviation (\(\sigma_{\bar{x}}\))**: - The sample standard deviation of the sample mean is calculated using the formula: - \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\) - Plugging in the values: \(\sigma_{\bar{x}} = \frac{18}{\sqrt{36}}\) - Simplify: \(\sigma_{\bar{x}} = \frac{18}{6} = 3\) #### Conclusion: - The sample mean (\(\mu_{\bar{x}}\)) is 81. - The sample standard deviation (\(\sigma_{\bar{x}}\)) is 3. By understanding these calculations, students can learn how to interpret and work with sampling distributions, an important concept in statistics.
Transcribed Image Text:### Determining Population and Sample Statistics #### Problem Statement: Determine \(\mu_{\bar{x}}\) and \(\sigma_{\bar{x}}\) from the given parameters of the population and sample size. Given Data: - Population Mean (\(\mu\)): 81 - Population Standard Deviation (\(\sigma\)): 18 - Sample Size (\(n\)): 36 #### Explanation: To solve this problem, we need to calculate the sample mean (\(\mu_{\bar{x}}\)) and the sample standard deviation (\(\sigma_{\bar{x}}\)) using the given population parameters. In sampling distribution theory, the sample mean and standard deviation for the sample mean are calculated as follows: 1. **Sample Mean (\(\mu_{\bar{x}}\))**: - The sample mean is equal to the population mean. - \(\mu_{\bar{x}} = \mu\) - Thus, \(\mu_{\bar{x}} = 81\). 2. **Sample Standard Deviation (\(\sigma_{\bar{x}}\))**: - The sample standard deviation of the sample mean is calculated using the formula: - \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\) - Plugging in the values: \(\sigma_{\bar{x}} = \frac{18}{\sqrt{36}}\) - Simplify: \(\sigma_{\bar{x}} = \frac{18}{6} = 3\) #### Conclusion: - The sample mean (\(\mu_{\bar{x}}\)) is 81. - The sample standard deviation (\(\sigma_{\bar{x}}\)) is 3. By understanding these calculations, students can learn how to interpret and work with sampling distributions, an important concept in statistics.
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