Question

Using the sample information given in Exercises $20-21$, give the best point estimate for the population mean $\mu$ and calculate the margin of error: A random sample of $n=75$ observations from a quantitative population produced $\bar{x}=29.7$ and $s^{2}=10.8$.

Name: Problem 21, Chapter 8: Introduction to Probability and Statistics
Uploaded: 2022-02-19T00:27:09-08:00
Duration: 1 min 56 s
Channel: Lucas Finney
Description: Using the sample information given in Exercises 20-21, give the best point estimate for the population mean μand calculate the margin of error: A random sample of n=75 observations from a quantitative population produced x̅=29.7 and s^2=10.8.

   Using the sample information given in Exercises $20-21$, give the best point estimate for the population mean $\mu$ and calculate the margin of error: 
A random sample of $n=75$ observations from a quantitative population produced $\bar{x}=29.7$ and $s^{2}=10.8$.

Introduction to Probability and Statistics

William Mendenhall,… 15th Edition

Chapter 8, Problem 21

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Solved by Expert Lucas Finney

02/19/2022

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We are given the sample size (n = 75), the sample mean (x̄ = 29.7), and the sample variance (s² = 10.8). Show more…

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Using the sample information given in Exercises $20-21$, give the best point estimate for the population mean $\mu$ and calculate the margin of error: A random sample of $n=75$ observations from a quantitative population produced $\bar{x}=29.7$ and $s^{2}=10.8$.

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Key Concepts

Point Estimate

A point estimate is a single numerical value used to estimate an unknown population parameter. In the context of estimating the population mean, the sample mean is commonly used because it is an unbiased estimator, meaning that on average, it equals the true population mean.

Margin of Error

The margin of error quantifies the range within which the true population parameter is expected to lie with a certain level of confidence. It is calculated using the critical value from the chosen confidence level along with the standard error, and it represents the maximum expected difference between the point estimate and the true parameter value.

Standard Error

The standard error is a measure of the variability of the sample mean from sample to sample. It is calculated by dividing the sample standard deviation by the square root of the sample size. The standard error is a key component in constructing the margin of error for confidence intervals.

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