A population has a standard deviation of σ=30. a. On average, how much difference should exist b

Name: Problem 5, Chapter 7: Essentials of Statistics for the Behavioral Science
Uploaded: 2023-10-04T17:53:21-08:00
Duration: 1 min 21 s
Channel: Sanchit Jain
Description: A population has a standard deviation of σ=30. a. On average, how much difference should exist between the population mean and the sample mean for n=4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n=25 scores? c. On average, how much difference should exist for a sample of n=100 scores?

step 1 according to the given question population mean mu is 40 and Sigma is 8 in the first case sample

Question

A population has a standard deviation of $\sigma=30$. a. On average, how much difference should exist between the population mean and the sample mean for $n=4$ scores randomly selected from the population? b. On average, how much difference should exist for a sample of $n=25$ scores? c. On average, how much difference should exist for a sample of $n=100$ scores?

   A population has a standard deviation of $\sigma=30$.
a. On average, how much difference should exist between the population mean and the sample mean for $n=4$ scores randomly selected from the population?
b. On average, how much difference should exist for a sample of $n=25$ scores?
c. On average, how much difference should exist for a sample of $n=100$ scores?

Essentials of Statistics for the Behavioral Science

Frederick J… 7th Edition

Chapter 7, Problem 5

Instant Answer

Solved by Expert Sanchit Jain

10/04/2023

Step 1

The SEM is a measure of how much the sample mean is expected to differ from the population mean. It is calculated using the formula: \[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \] where $\sigma$ is the population standard deviation and $n$ is the sample size. Show more…

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A population has a standard deviation of $\sigma=30$. a. On average, how much difference should exist between the population mean and the sample mean for $n=4$ scores randomly selected from the population? b. On average, how much difference should exist for a sample of $n=25$ scores? c. On average, how much difference should exist for a sample of $n=100$ scores?

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Key Concepts

Standard Error of the Mean

The standard error of the mean represents the average amount by which a sample mean is expected to differ from the population mean. It is calculated as the population standard deviation divided by the square root of the sample size. This measure quantifies the precision of the sample mean as an estimate of the true population mean and decreases as the sample size increases.

Sampling Distribution of the Mean

The sampling distribution of the mean is the probability distribution formed by the means obtained from many samples drawn from the same population. Its center is the population mean, and its spread is defined by the standard error of the mean. This concept is fundamental in inferential statistics because it helps explain how sample means become more reliable estimates of the population mean as the sample size increases.

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