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Business Statistics M) The Retailers Anti-Theft Alliance (RATA) published a stody that claimed the causes of disappearance of inventory in retail stores were 30 percent shoplifting, 50 percent employee theft, and 20 percent faulty paperwork. Michael, the manager of the Melodic Kortholt Outlet, performed an audit of the disappearance of 80 items and found the frequencies shown below. Reason Shoplifting Employee Theft Poor Paperwork Frequency 32 38 10 Published Percentage 30% 50% 20% Part A: Michael would like to know if his store's experience differs from a pattern published. What is the appropriate tool for this analysis and why? Be as specific as possible. Part B: What is the conclusion at 10% significance level? Part C: Provide a brief interpretation of the result. 1 2) Best Food is developing a new frozen pizza product, and it asked a random sample of 30 customers to rate the product quality (maximum score is 100 points). The company also observed whether the customer bought the product at the end. Customer Score Buy or Not (Buy-1, Not buy-O) 1 16 2 20 3 27 4 29 5 38 6 46 7 46 8 47 I 9 49 10 50 11 52 12 53 1 13 55 14 59 1 15 64 16 68 1 17 72 18 74 1 19 76 20 80 1 21 82 1 22 85 1 23 87 24 88 1 25 88 1 26 89 1 27 90 28 91 1 29 94 1 30 96 1 Part. A: Write the estimated logistic regression equation relating x toy. Part B: Based on the equation in part A), estimate the probability that a customer who gives a score of 90 points will buy the product. Part C: Based on the equation in part A), a customer will have a 0.80 or higher probability of buying if the score is approximately or higher. What is the value of this score? Note: You may round your ansuer to the integer. 2

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1)

Part A:

The appropriate tool to analyze this data is using chi-square test for goodness of fit. In this case we want to see whether there is any significant difference between the observed value and expected value, so the best test is chi-square test to test this hypothesis. It is based on the below Hypothesis and formula:

Null Hypothesis (Ho): There is no statistically significant difference in the pattern published for the causes of disappearance of inventory in retail stores. It means that observed frequency and expected frequency is same for the causes of disappearance of inventory in retail stores.

Alternative Hypothesis (Ha): There is a statistically significant difference in the pattern published for the causes of disappearance of inventory in retail stores. It means that observed frequency and expected frequency is not same for the causes of disappearance of inventory in retail stores....

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