M670_8_2(Hypothesis Testing II)

# M670_8_2(Hypothesis Testing II) - Hypothesis Testing...

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1 Hypothesis Testing II (Comparison of Two Populations) k MGMT 670: Business Analytics Krannert School of Management Purdue University

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2 Three Situations § Population Mean Paired (matched) samples Independent samples Equal variances Unequal variances
3 Paired vs. Unpaired Test § Paired Test (Matched Samples): Select a simple random sample and let every person in the sample rate each of the two flavors in a random order. § Unpaired Test (Independent Samples): Select two simple random samples and let each group rate only one flavor. § Paired test tends to remove much of the extraneous variations (e.g., variation in people and experimental conditions) § Suppose that a taste test of two flavors is carried out.

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4 Difference Between the Means of Two Populations: Matched Samples § With a matched-sample design each sampled item provides a pair of data values. § By considering the difference of each pair of the data values, we can apply the same procedures as the single population case.
5 Example: Express Deliveries To test the delivery times of two express delivery services, UPX (United Parcel Express) and INTEX (International Express), two reports were sent to a random sample of ten district offices with one report carried by UPX and the other report carried by INTEX. Do the data that follow indicate a difference in mean delivery times for the two services?

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6         Delivery Time (Hours) District Office UPX INTEX Difference Seattle 32 25 7 Los Angeles 30 24 6 Boston 19 15 4 Cleveland 16 15 1 New York 15 13 2 Houston 18 15 3 Atlanta 14 15 -1 St. Louis 10 8 2 Milwaukee 7 9 -2 Denver 16 11 5 Example: Express Deliveries
7 Minitab Procedure

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8 Select Columns and Set Options
9 Minitab Printout Paired T-Test and CI: UPX, INTEX Paired T for UPX - INTEX N Mean StDev SE Mean UPX 10 17.70 7.87 2.49 INTEX 10 15.00 5.64 1.78 Difference 10 2.700 2.908 0.920 95% CI for mean difference: (0.620, 4.780) T-Test of mean difference = 0 (vs not = 0): T-Value = 2.94 P-Value = 0.017 Since p-value =                         there is ________________to believe that the mean delivery  times of the services are different.

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10 Difference Between the Means of Two Populations: Independent Samples Sample 1 1 1 1 , , n s x ? 2 1 μ μ- Sampling Distribution of Population 1 m 1, s 1 Population 2 m 2, s 2 Sample 2 2 2 2 n , s , x x ¯ 1 - x ¯ 2
11 Hypothesis Tests About the Difference μ 1 - 2: Standard Deviation Unknown Large-Sample Case ( n 1 and n 2  30) or Normal Population § Two cases to consider Unequal population variances. When Equal population variances. Or, when 2 2 2 1 σ σ≠ 2 2 1 2 =

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12 Example: Start-up Owner’s Equity § Two populations 1. Small business firms that have resulted in
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M670_8_2(Hypothesis Testing II) - Hypothesis Testing...

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