MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Finding the Confidence Interval for a Population Mean** In this example, we are tasked with finding the confidence interval for a population mean \( \mu \) using the given values and to interpret the interval accurately. The specific values provided are: - Significance level (\( \alpha \)): 0.05 - Sample size (\( n \)): 85 - Sample mean (\( \bar{x} \)): 66.6 - Sample variance (\( s^2 \)): 2.38 **Steps:** 1. **Calculate the Confidence Interval:** - Determine the confidence level, which is \( 1 - \alpha = 0.95 \) or 95%. - Use the given sample size, mean, and variance to find the confidence interval bounds. - Round your answers to two decimal places. 2. **Interpret the Interval:** The correct interpretation of the constructed confidence interval should be chosen from the following options: - There is a 5% chance that an individual sample mean will fall within the interval. - In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean. - 95% of all values will fall within the interval. - There is a 95% chance that an individual sample mean will fall within the interval. - In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean. **Explanation:** Confidence intervals provide a range within which we expect the true population parameter to lie. It is a reflection of statistical confidence based on sample data, without guaranteeing the parameter's location within that range for a single interval but rather across many different samples and intervals.
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Transcribed Image Text:**Finding the Confidence Interval for a Population Mean** In this example, we are tasked with finding the confidence interval for a population mean \( \mu \) using the given values and to interpret the interval accurately. The specific values provided are: - Significance level (\( \alpha \)): 0.05 - Sample size (\( n \)): 85 - Sample mean (\( \bar{x} \)): 66.6 - Sample variance (\( s^2 \)): 2.38 **Steps:** 1. **Calculate the Confidence Interval:** - Determine the confidence level, which is \( 1 - \alpha = 0.95 \) or 95%. - Use the given sample size, mean, and variance to find the confidence interval bounds. - Round your answers to two decimal places. 2. **Interpret the Interval:** The correct interpretation of the constructed confidence interval should be chosen from the following options: - There is a 5% chance that an individual sample mean will fall within the interval. - In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean. - 95% of all values will fall within the interval. - There is a 95% chance that an individual sample mean will fall within the interval. - In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean. **Explanation:** Confidence intervals provide a range within which we expect the true population parameter to lie. It is a reflection of statistical confidence based on sample data, without guaranteeing the parameter's location within that range for a single interval but rather across many different samples and intervals.
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