Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

A sample of size 400 has mean =6.0. Can it be regarded as a sample from a large population with mean 6.25 inches and standard deviation 2.25 inches ? using α=0.05

Sagot :

The value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.

What is the standard deviation?

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

The standard error of the estimated mean:

[tex]\rm = \dfrac{2.5}{\sqrt{400}}[/tex]

= 0.1125

x = 6.0–6.2 = 0.2

[tex]\rm Z = \dfrac{0.2}{0.1125}[/tex]

Z = 1.778

This is not significant at the 5% level.

This would have been significant at the 5% level if the same sample means had been found using a sample size of merely 500.

Thus, the value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.

Learn more about the standard deviation here:

brainly.com/question/12402189

#SPJ1