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MGMT305-Lec7

# S weare95confidentthatthedifferencebetweenthe

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Unformatted text preview: e of µ1 ­ µ2? Slide 13 Example 2: Specific Motors s 95% Confidence Interval Estimate of the Difference Between Two Population Means: Small­Sample Case We will make the following assumptions: • The miles per gallon rating must be normally distributed for both the M car and the J car. • The variance in the miles per gallon rating must be the same for both the M car and the J car. Using the t distribution with n1 + n2 ­ 2 = 18 degrees of freedom, the appropriate t value is t.025 = 2.101. We will use a weighted average of the two sample variances as the pooled estimator of σ 2. Slide 14 Example 2: Specific Motors (b) Construct the 95% Confidence Interval Estimate of the Difference Between Two Population Means. s We are 95% confident that the difference between the mean mpg ratings of the two car types is from Slide 15 Summary of Interval Estimation Procedures About the Difference in Popln. Means Slide 16 σ1, σ2 KNOWN: Hypothesis Tests About µ 1 ­ µ 2: Independent Samples (Large­Sample and Small­Sample Cases) s Hypotheses H0: µ1 ­ µ2 < 0 H0: µ1 ­ µ2 > 0 H0: µ1 ­ µ2 = 0 Ha: µ1 ­ µ2 > 0 Ha: µ1 ­ µ2 < 0 Ha: µ1 ­ µ2 ≠ 0 Test Statistic n1 > 30 n2 < 30 s Invoke CLT Assume Normal Dist. ( x1 − x2 ) − ( µ1 − µ 2 ) ( x1 − x2 ) − ( µ1 − µ 2 ) z= z= 2 2 2 σ1 n1 + σ 2 n2 σ1 n1 + σ 2 n2 2 NOTE: Use z distribution Slide 17 σ 1, σ 2 KNOWN (Large and Small Samples) s Rejection Rule z > zα , I. Reject if H 0 : µ1 − µ 2 ≤ 0 Or, p­value = P (Z>z) < α. H 0 : µ1 − µ 2 ≥ 0 z < − zα , II. Reject if Or, p­value = P (Z<z) < α . z < − zα / 2 H 0 : µ1 − µ2 = 0 III. Reject if Or z > zα / 2 , α. Or, p­value = 2P (Z>|z|) < Slide 18 σ1, σ2 UNKNOWN: Hypothesis Tests About µ 1 ­ µ 2: Independent Samples (Large­Sample Case: n1 > 30 and n2 > 30) s Hypotheses H0: µ1 ­ µ2 < 0 H0: µ1 ­ µ2 > 0 H0: µ1 ­ µ2 = 0 Ha: µ1 ­ µ2 > 0 Ha: µ1 ­ µ2 < 0 Ha: µ1 ­ µ2 ≠ 0 s Test Sta...
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