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Managerial Statistics, A Case Base Approach by: Klibanoff, Sandroni, Moselle, Saraniti

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Managerial Statistics, A Case Base Approach by: Klibanoff, Sandroni, Moselle, Saraniti

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    1. Summer 2009 Clayton State University School of Business Dr. Reza Kheirandish 1 Managerial Statistics, A Case Base Approach by: Klibanoff, Sandroni, Moselle, Saraniti

    2. Chapter Two 2 Distributions and Hypothesis Testing. Objective: Introduce Hypothesis Testing and Kstat. Cases: Test Marketing Gender Gap Asset Return

    3. IQ distribution is Normal 3

    4. Typical and Abnormal Values 4

    5. Test Marketing 5 Question: Whether or not to introduce a new color option in a computer. Profitable only if average sales (m ) greater than 275 units per week. Data Test were conducted over 36 weeks.

    6. 6

    7. Sales Distribution 7

    8. Test Marketing (Formally) 8 m : average sales per week. Ho: m is smaller than 275. Ha: m is greater than 275.

    9. Computations 9 Test Statistic =

    10. Conclusions 10 1 minus the p-value is maximum confidence on the alternative hypothesis. Low p-value (e.g. 4.379%) means reject the null. Average Weekly Sales will exceed 275

    11. Justice and Hypothesis Testing 11 Facts 50% of eligible jurors were African Americans. In a panel of 80, 4 were African Americans. Prosecution: There is a “Bias”. Defense: It happened by “Chance”.

    12. Resolution 12 Prosecution: Give the defense the benefit of the doubt. Assume random selection of jurors. The chance of this configuration is almost zero, that is, P-value is: 0.000000000000000414

    13. Summary 13 Ho (Null Hypothesis) Jurors selected at random Ha (Alternative Hypothesis) Bias in juror selection Low p-value ? Reject Null. Accept Alternative. High p-value ? Test is inconclusive.

    14. Consumer Packaging - Part II 14 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.

    15. 15 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?

    16. Consumer Pack Data Summary 16

    17. Hypothesis testing 17 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)

    18. 18

    19. Difference in means (m1 - m2 ) 19 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. s1 and s2 sample standard deviations (n1= n2 = 36, s1 = 53.1, s2 = 47.8)

    20. Distribution 20

    21. Confidence Interval 21 1) Choose a Probability (95%). 2) Center the CI at estimate. 3) Add and Subtract Margin of Error. Get the Upper and Lower level.

    22. Confidence Interval 22

    23. 23 Margin of Error = the Standard Deviation Multiplied by T-value. T-value in the t-table. For 95% is 1.99 (note: degree of freedom is 36+36-2=70) Margin of Error = 1.99* 11.91 = 23.76. (27.80 – 23.76, 27.80 + 23.76) = (4.04 , 51.56) With 95% of confidence, the true difference in the means is between 4.04 and 51.56.

    24. Confidence Interval 24

    25. The Gender Gap 25 Before the California Election, Lieutenant Governor Cruz Bustamante was the first choice of 26% of the men and 35% of the women. This was observed in a sample of 505 people. Is this difference statistically significant? Is it caused by sampling error?

    26. Population Proportions 26 Pm = proportion of men who prefer Bustamante. Pw = proportion of women who prefer Bustamante. Mean Difference Pw - Pm = 0.09 Standard Deviation 0.04078 is 2.207 standard deviations from 0.09 p-value is close to ZERO.

    27. Conclusion 27 The difference is genuine. We are approximately 97.3% confident of a gender gap.

    28. Asset Returns 28 Are average returns on the Japanese Stock market greater than in the US? Are the returns on the stock market greater than 10 years ago? Compare returns from 26 to 36 with returns from 36 to 46 in the US.

    29. 29 Monthly Returns on US stock

    30. Asset Returns Data Summary 30

    31. Asset Returns (cont) 31

    32. Asset Returns on the US 32 The average monthly return during 36-46 is much greater than during 26-36. The difference is not statistically significant (p-value = 0.67.) The stock market is too volatile. This test for structural change is inconclusive.

    33. Chapter Two: Take Away 33 Hypothesis testing: intuition and 4 steps What are H0 and Ha; how to set them up. What is the t-value/test statistic (meaning and calculation) What is the p-value of a hypothesis test What is the significance level (?) and how to decide on the result HT about population averages see testmarket example Confidence Intervals How to use Excel/Kstat Loading data files, interpreting Univariate Statistics Functions TDIST, TINV, NORMSDIST, NORMSINV

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