Question

Hypothesis Testing:

Use of Multiple Sample Hypothesis Tests

In your chosen field, when might you want to know the mean differences between two or more groups? Please describe the situation, including how and why the hypothesis test would be used.

Answer 1

Hypothesis Testing:

The hypothesis testing assess the two mutually exclusive statement (Null and Alternate hypothesis) to test which statement is best suited with the sample groups. The pupose of the test is to evaluate whether the observed differences among the sample groups are statistically significant.

The example:

A magazine issuer wants to compare the four different design for a magazine that will be offered for sale. The issuer is interested in whether there is a design that perform better in term of sale. To examine this issuer randomly select the store and assign randomly one of the design and record the sell for each store for a period.

How and why the hypothesis test would be used:

To understand why the hypothesis test is needed lets take the above example where the magazine issuer interested in the mean sale of the four different design of magazine. Since the issuer are looking at the sample rather than the entire population. The sample mean of the sale may be different from the population mean.A hypothesis test helps here to test the likelihood of this possibility.

Here hypothesis testing answer the question "Whether all the groups are from same population means?". In other words whether the differences among sample means are statistically significant or large enough. The side by side box plot can be used to see the difference between means.

This figure of side by side box plot shows that there is larger within group variance of means but small between group variance. We can say that there is no significant difference among means.

This figure of side by side box plot shows that there is small within group variance of means but larger between groups variance. We can say that there is statistically significant difference among means.