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Template for a Confidence Interval: Variable:_________________________ Parameter: ________________________ Point Estimate: ________________________ Standard Error ________________________ Inference: Estimation Formula (Page Number)________________________ Formula Substitution: Conclusion: We are ____% confident CONFIDENCE that the ______________________ PARAMETER ____________________________ DEPENDENT VARIABLE falls in the range:________________ RANGE Example Using Template for a Confidence Interval: You wish to estimate the average annual return on a population of stocks. From a random sample of size 50, you find an average of 14.75 and a standard deviation of 8.18. With 95% confidence what is the average annual return? Dependent Variable: annual return Parameter: Point Estimate x = 14.75 Standard Error Sx = Inference: Estimation s 8.18 = =1.1569 n 50 Formula (Page Number) ________ Formula ( x ) (tn-1,/2) S x Substitution: 14.75 ± t49, 0.025 (1.1569) 14.75 ± 2.009 (1.1569) 14.75 ± 2.32 12.43 to 17.07 Conclusion: We are 95% confident that the average annual return falls in the range: 12.43 to 17.07 percent. or Conclusion: We are 95% confident that the average annual return is 14.75 with a margin of error of ± 2.32 CONFIDENCE PARAMETER VARIABLE RANGE CONFIDENCE PARAMETER VARIABLE ESTIMATE VALUE MARGIN OF ERROR Template for a Hypothesis Test: Variable:_________________________ Parameter: ________________________ Point Estimate: ________________________ Standard Error ________________________ Inference: Hypothesis Test Ho: _________ Rejection Region: Reject Ho if Ha: _________ _________________________ Test Statistic: Formula (page)___________ Formula Substitution: Conclusion: At = _____ SIGNIFICANCE LEVEL we can (not) say that DECISION that the ______________________ PARAMETER ____________________________ DEPENDENT VARIABLE ____________________________ PARAMETER VALUES IN Ha Example Using Template for a Hypothesis Test: In the past the machines you use can process 450 items on average per day. A new company says that its machine will outperform your current ones. You take a random sample of size 50 and find a sample mean of 460.38 with a standard deviation of 38.83. Is there evidence that the new machine is better? Variable: number of packages processed Parameter: Point Estimate x = 460.38 Standard Error Sx = Inference: s 38.83 = = 5.4914 n 50 Hypothesis Test Ho: ≤ 450 Rejection Region: Reject Ho if Ha: > 450 t* > t(n-1,) = t (49, 0.05, ) = 1.676 Test Statistic: Formula (page) _______ Formula t* = ( x - ) / S x Substitution: t* = (460.38-450) / (1.676) = 1.89 Conclusion: At = 0.05 we can say that that the mean number of packages processed is greater than 450 packages. SIGNIFICANCE LEVEL DECISION PARAMETER VARIABLE PARAMETER VALUES IN Ha