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Statistics Quick Overview

Statistics Quick Overview. Class #4. 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. . Consumer Packaging - Part II.

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Statistics Quick Overview

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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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