For this problem collect data on any variables of interest s

For this problem, collect data on any variables of interest (sample size for each group of the two groups n=>30) and perform a two-sided signifcance test for comparing two independent populations means. You can simulate your own data.

Address the following: a brief introductory paragraph describing the problem

Set up your framework in a null and alternative hypothesis using symbols and notation.

A paragraph describing how you collected the data (number of observations, time of day,etc) Present this data in a table

Please plot the means of the two samples using Excel.

A section explaining the results of the analysis (calculated statistics, and p-values).

Based on what you find, state your decision (reject or fail to reject the null hypothesis) and conclusion (whether there is sufficient or insufficient evidence for alternative hypothesis.

Finally, describe how you would change the experimental desing to become dependent or related samples.

Solution

Given that mu = 150, sigma = 21

For answering this question we recollect the central limit theorem for distributions.

As sample size becomes large due to law of large numbers, the sample mean approximates to normal distribution irrespective of the underlying distribution originally.

Hence no assumption was made.

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C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.

Central limit theorem applies only to large numbers and n should be atleast 30. If less than 30, better use t test.

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