KWeights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n= 15, are randomly collected and the sample means are found. Is it correct toconclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.Choose the correct answer below.OA. Yes; the sample size must be over 30 for the sample means to be normally distributed.OB. No; as long as more than 30 samples are collected, the sample means will be normally distributed.OC. No; the samples are collected randomly, so the sample means will be normally distributed for any sample size.OD. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size.

Answered: K dogs, each of size n=15, are randomly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

K
Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n= 15, are randomly collected and the sample means are found. Is it correct to
conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.
Choose the correct answer below.
OA. Yes; the sample size must be over 30 for the sample means to be normally distributed.
OB. No; as long as more than 30 samples are collected, the sample means will be normally distributed.
OC. No; the samples are collected randomly, so the sample means will be normally distributed for any sample size.
OD. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size.

Expert Solution

Step 1

Central limit theorem:

If the size of the samples taken from the population are sufficiently large (>30) then the mean of all the samples taken would be approximately same as the population mean.

The sampling distribution of the sample mean is approximated to normal if,

The population is normal
The sample size is large which is greater than 30.
If the original population doesn’t’ follows normality, for the large n, the sample mean also follows normality.
The formula of the standard deviation of sampling distribution is σ/√n if n is large even though population does not follows normality.