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Statistical analysis of variance tests and quality of group means

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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 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.

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

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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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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