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BUS310_L20_3.31.11

# BUS310_L20_3.31.11 - Inferential Statistics Simple...

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Lecture 20: Inferential Statistics / Simple Regression Chapter 12 (12.1, 2) 22
Review Handout Chapters 9, 10, 11 PS5 PS6 New Material: Simple Linear Regression (Chapter 12 – next 3 lectures) How to use regression analysis to predict the value of a dependent variable based on an independent variable (e.g., sales, based on store size) 33

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PS5 44
PS5 (Chapter 9) 1. Problem 9.67 (2 points) An audit was conducted on a sample of 75 reimbursements by Medicare to physicians , with the following results: -. The average amount of reimbursement was X = \$93.70, (SD=\$34.55) . -. In 12 of the 75 office visits , an incorrect reimbursement amount was provided. a) At the 0.05 level of significance, is there evidence that the population mean reimbursement was less than \$100 ? d) What is your answer to a) if the sample mean equals \$90 ? c) Discuss the underlying assumptions .

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P-value: 0.059284 We are 94.07% confident that the average amount of all Medicare reimbursements is less than \$100. There is not enough evidence to reject H0 (the mean of all reimbursements is equal or greater than \$100.) Hypotheses: H1: μ < 100 H0: μ ≥ 100 a) At the 0.05 level of significance, is there evidence that the population mean reimbursement was less than \$100 ?
d) What is your answer to a) if the sample mean equals \$90 ? Hypotheses: H1: μ < 100 H0: μ ≥ 100 Now the sample mean is lower, which should increase our confidence that the population mean is below \$100. P-value: 0.00719 & Actual Confidence (1 - P-value) = 99.28% Now we are more than 99% confident that the average reimbursement amount from Medicare is less than \$100. Reject H0 .

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c) Discuss the underlying assumptions for the test in a). We have to check the assumption of Normality to determine whether the test is valid. The assumption of normality is met, because the sample size is large (greater than 30) with n = 75).
Sample proportion is 16% (=12/75) Based on these data, how confident are you that the population proportion is greater than 10%? Hypotheses: H1: π > 0.1 H0: π ≤ 0.1 P-value: 0.0416 Actual Confidence (1 - P-value) = 95.84% We are 95.8% confident that the proportion of incorrect reimbursements from Medicare (of all reimbursements) is greater than 0.10 (10%). Reject the Null Hypothesis. b) At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population was greater than 0.10 ?

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(=15/75). Our confidence should increase, that the population proportion is higher than 10%. H1: π > 0.1 H0: π ≤ 0.1 P-value: 0.00195 Actual Confidence (1 - P-value) = 0.99805 = 99.81% We are 99.8% confident that the proportion of incorrect reimbursements in the population was greater than 0.10. Reje
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BUS310_L20_3.31.11 - Inferential Statistics Simple...

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