# Statistical analysis of variance tests and quality of group means

"Discounts and Sales"

Analysis of variance tests the equality of group means simultaneously. If you reject the null hypothesis and infer that the group means are not equal, you still cannot say which particular means are not equal and which ones are. Additional tests are needed.

Question

Test the hypothesis that the average sales in stores offering 40% discount on chocolate bars were equal to the average sales in stores offering 20% discount. Can you conclude that 40% discount generates more sales of chocolate bars than 20% discount?

Steps:

• Locate averages of the two groups you are asked to compare and find their difference. Use may use table "Summary" of the ANOVA output.

• Locate the pooled variance in the "Anova" table of the output (it is located in a cell corresponding to column 'MS' and row 'Within Groups') and compute the pooled standard deviation by taking square root.

• Compute the standard error of the test statistics by multiplying the pooled standard deviation and the square root of 2/20.

• Calculate the t-statistic by dividing the mean difference on the standard error.

• Test the hypotheses about equality of two means using t-test and using t*=1.664 as the critical value. Remember that you reject null hypothesis if the absolute value of your test statistic exceeds the critical value.

• Make inference about the equality of the two means.

https://brainmass.com/statistics/analysis-of-variance/statistical-analysis-variance-tests-quality-group-means-263660

#### Solution Preview

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"Discounts and Sales"

Analysis of variance tests the equality of group means simultaneously. If you reject the null hypothesis and infer that the group means are not equal, you still cannot say which particular means are not equal and which ones are. Additional tests are needed.

Question

Test the hypothesis that the average sales in stores offering 40% discount on chocolate bars were equal to the average sales in stores offering 20% discount. Can you conclude that 40% discount generates more sales of chocolate bars than 20% discount?

Steps:

• Locate ...

#### Solution Summary

This post makes an inference about the equality of the two means.