# Comparing Samples Using F-Hypothesis Test

It was the year of no weekends, no vacations and no birthdays. I learned a lot at work and earned myself a good bonus. It has been a long time dream of mine to start my own business. I decided to give it a shot and set up a small fashion store in my garage operating only on the weekends.

The previous month, I asked my friends (who also happen to be very famous – read fictitious) to rate my collections. They rate from 1 star to five stars and my collections get around 3.0.

This month, I collected clothes from five different suppliers and made it more diverse. I got the ratings for my new collection.

I collect 60 sample ratings from an old collection and 40 sample ratings from the second collection to compare how varied the ratings are.

A variance is a measure of how far each value is set from the mean.

We use F test to compare variances of two populations.

The null hypothesis is that the variance of two sets of ratings is equal.

The alternate hypothesis is that the variance of two sets of ratings is not equal.

The following table is a subset of the data. Please download the workbook from the link below to gain access to the entire work.

F – Test Workbook

Using the Data Analysis tool in the ‘Data’ tab of the ribbon, we obtain the following information.

Variable 1 is New Ratings

Variable 2 is Old Ratings

The population with the higher variance is to be made Variable 1 while using Excel.

F Value = Variance 1 / Variance 2

F critical from the F table = 1.59

We can accept the null hypothesis only if F > F critical.

Therefore, we cannot reject the null hypothesis in this case. The variances of the two populations are equal.

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