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Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

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 22PFA
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### Estimating the Margin of Error for a Population Proportion **Problem Statement:** Assume that a sample is used to estimate a population proportion \( \mu \). Find the margin of error \( M.E. \) that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. **Instructions:** Report the margin of error (M.E.) accurate to one decimal place because the sample statistics are presented with this accuracy. \[ M.E. = \boxed{} \] **Additional Notes:** - Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. This exercise involves calculating the margin of error for the given sample statistics. The critical value for a 90% confidence level is generally 1.645 when using the z-distribution for large samples. To find the margin of error, use the formula: \[ M.E. = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \] Where: - \( z \) is the critical value for the desired confidence level, - \( \sigma \) is the standard deviation, - \( n \) is the sample size. ### Example Calculation (Not part of the original problem statement) For illustrative purposes, assume the critical value \( z \) for a 90% confidence interval is 1.645. \[ M.E. = 1.645 \times \left( \frac{17.5}{\sqrt{709}} \right) \] Perform the computation step-by-step to find the numerical value.
Transcribed Image Text:### Estimating the Margin of Error for a Population Proportion **Problem Statement:** Assume that a sample is used to estimate a population proportion \( \mu \). Find the margin of error \( M.E. \) that corresponds to a sample of size 709 with a mean of 42.1 and a standard deviation of 17.5 at a confidence level of 90%. **Instructions:** Report the margin of error (M.E.) accurate to one decimal place because the sample statistics are presented with this accuracy. \[ M.E. = \boxed{} \] **Additional Notes:** - Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. This exercise involves calculating the margin of error for the given sample statistics. The critical value for a 90% confidence level is generally 1.645 when using the z-distribution for large samples. To find the margin of error, use the formula: \[ M.E. = z \times \left( \frac{\sigma}{\sqrt{n}} \right) \] Where: - \( z \) is the critical value for the desired confidence level, - \( \sigma \) is the standard deviation, - \( n \) is the sample size. ### Example Calculation (Not part of the original problem statement) For illustrative purposes, assume the critical value \( z \) for a 90% confidence interval is 1.645. \[ M.E. = 1.645 \times \left( \frac{17.5}{\sqrt{709}} \right) \] Perform the computation step-by-step to find the numerical value.
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