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# Analysis of variance (ANOVA) and F test

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Please, perform an F test for columns A (gender), B (age), and E (overall satisfaction) (in the attached spreadsheet)

Please use all the data rows for each of these three columns. (from the Excel table attached)

For this and any hypothesis test, I want you to number the five steps as in the book.

Here are the 5 steps:

1. State the Hypothesis and identify the claim

2. Find the critical value

3. Compute the test value.

4. Make the decision

5. Summarize the results

Please provide the following summary table.
Null and Alternative Hypotheses H0:
H1:
Significance Level
Degrees of freedom
Critical Value &#945;=
df=
tcrit=
Test Value t=
Decision

Then run an ANOVA and clearly state each step and the formula used for each step.

Then use the Table below: (enhance if you must to fit the data)

Source Degrees of Freedom Sum of Squares Mean Square F value
Between
Within
Total

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#### Solution Summary

This solution shows how to use hand calculations to to do an analysis of variance.

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## ANOVA Problem

When we want to test two samples to determine if it is likely that the population means (estimated by the sample means) are different, we typically use a t-test. If the samples are large, we can also use a z-test. (Note that the formulas for computing s, t and/or z in the case of a two-sample test are different than the formulas for computing the same values in a one-sample test. Use Excel data analysis to conduct tests comparing two sample means.)

Using ANOVA (short for Analysis of Variance), however, we can test 3 or more sample means to determine if at least one of the sample means comes from a population with a mean that is significantly different from all of the others in the test. We actually do this by estimating a combined population variance two different ways and comparing the two estimates (the ratio of these two variance estimates follows the so-called "F distribution").

Question:

Why do we need a new test method to compare the means of 3 or more populations? Why can't we just use a series of z-tests or t-tests to compare all of the possible pairs of population means to see if one (or more) is different?

Most of the testing is to determine one or two things:

1. Is there a statistically significant difference between two or more population means? (based on comparison of 2 or more sample means)

2. Is there a statistically significant relationship between two or more variables? We can use regression analysis or chi-square tests to answer this second question.)

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