A random sample is selected from a population with mean μ=200 and standard deviation σ=15. Deter

Name: Problem 11, Chapter 12: Statistics Learning From Data
Uploaded: 2023-06-08T17:50:09-08:00
Duration: 4 min 39 s
Channel: Prabhakar Kumar
Description: A random sample is selected from a population with mean μ=200 and standard deviation σ=15. Determine the mean and standard deviation of the sampling distribution of x̅ for each of the following sample sizes: a. n=12 d. n=40 b. n=20 e. n=90 c. n=25 f. n=300

step 1 In this question, we have been given to calculate the value of mean of the sampling distribution

Question

A random sample is selected from a population with mean $\mu=200$ and standard deviation $\sigma=15$. Determine the mean and standard deviation of the sampling distribution of $\bar{x}$ for each of the following sample sizes: a. $n=12$ d. $n=40$ b. $n=20$ e. $n=90$ c. $n=25$ f. $n=300$

   A random sample is selected from a population with mean $\mu=200$ and standard deviation $\sigma=15$. Determine the mean and standard deviation of the sampling distribution of $\bar{x}$ for each of the following sample sizes:
a. $n=12$
d. $n=40$
b. $n=20$
e. $n=90$
c. $n=25$
f. $n=300$

Statistics Learning From Data

Thomas H. Short,… 2nd Edition

Chapter 12, Problem 11

Instant Answer

Solved by Expert Prabhakar Kumar

06/08/2023

Step 1

According to the Central Limit Theorem, the sampling distribution of the sample mean $\bar{x}$ for a sufficiently large sample size will be approximately normally distributed, regardless of the shape of the population distribution. The mean of the sampling Show more…

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A random sample is selected from a population with mean $\mu=200$ and standard deviation $\sigma=15$. Determine the mean and standard deviation of the sampling distribution of $\bar{x}$ for each of the following sample sizes: a. $n=12$ d. $n=40$ b. $n=20$ e. $n=90$ c. $n=25$ f. $n=300$

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Key Concepts

Standard Error

The standard error is the standard deviation of the sampling distribution of the sample mean. It quantifies the variability of the sample mean around the population mean and is calculated as the population standard deviation divided by the square root of the sample size.

Central Limit Theorem

The Central Limit Theorem states that, for a sufficiently large sample size, the distribution of the sample mean will approximate a normal distribution, regardless of the shape of the population distribution. This theorem underpins the use of normal probability models in inference even when the underlying population is not normally distributed.

Sampling Distribution of the Sample Mean

This concept refers to the probability distribution of all possible sample means taken from a population. It describes how the sample mean varies from sample to sample, and its properties are key in making inferences about the population mean.

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