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Consumer Packaging - Statistical Comparison of two Packages

Analyzing sales data from 36 districts for two packaging options to determine which is more attractive to consumers. Statistical tests to compare means and assess confidence levels. Suggestions for further testing and decision-making.

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Consumer Packaging - Statistical Comparison of two Packages

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  1. Statistics Quick Overview Class #4

  2. Consumer Packaging - Part II • Which (among two) package makes a product more attractive? • Data: 36 sales districts selected for each package. • Problem: The product is sold in other districts. We cannot test them all.

  3. Consumer Packaging - Part II • Idea: Look at sample means. • Package 1 has higher average sales than package 2 in the sample. • Problem: The sample may not be representative. • Are we sure that package 1 is better?

  4. Consumer Pack Data Summary

  5. Are we done? Pack 1 > Pack 2 • Pack #1 is much larger than Pack #2 • We have other decisions • Continue the test for another month • Expand the number of markets • Maybe there are some other cost considerations

  6. Hypothesis testing m1 average sales using package 1 m2 average sales using package 2 Ho: m1≤m2 (package 1 is worse) Ha: m1>m2 (package 1 is better)

  7. p-value = 0.011. We are 98.9% confident that package 1 is better.

  8. Difference in means (m1-m2 ) Estimated at 290.55 – 262.75 = 27.80 (in favor of pack 1) Standard Deviation ((s1) 2/n1+ (s2)2/n2) 0.5 =11.91 n1 and n2 sample sizes. s1and s2sample standard deviations (n1= n2 = 36, s1 = 53.1, s2 = 47.8)

  9. Hypothesis testing Ho: m1 - m2≤ 0 (package 1 is worse) Ha: m1 - m2> 0 (package 1 is better) Test statistic = TDIST = (2.334, 70, 1) = .001124 Reject the Null 27.80 – 0 = 2.334 11.91

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