Chart 11-1: Minitab Difference Between 2 Population Means Alternative = nature of H1 (in our case, greater than) Click Samples in different columns If we assume that population variances are equal, then select Assume equal variance. (In our example, we do not select this.) Input Confidence Level =(1α) × 100 (95.0 in our case) Input First =C1, Second = C2 Click OK Click Stat Click Basic Statistics Input the first sample data in column C1 and the second in column C2 Click 2-Sample t... Chart 11-1: Minitab Difference Between 2 Population Means

Chart 11-2: Excel Difference Between 2 Population Means Click t-Test: Two-Sample Assuming Unequal Variances (If we know that the two population variances are equal, choose Two-Sample Assuming Equal Variances.) Click OK Input Variable 1 Range = range of sample data 1 in column A, Variable 2 Range = range of sample data 2 in column B Click OK Click Tools Input Alpha = value of level of significance (In our case, 0.05) Input Hypothesized Mean Difference = test value of (μ1μ2) (In our case, 60) Input the sample data 1 in column A and the Sample data 2 in column B Click Data Analysis Chart 11-2: Excel Difference Between 2 Population Means

Chart 11-3: Minitab Paired T-Test Click Options Input the two sample data in two columns of the worksheet Click Paired t Click Basic Statistics Click Stat Click OK Input Confidence Level =(1)×100 (95.0 in our case) Input Test mean = test value of (µ1µ2) ( = 0 in our case) Click OK Input names of columns containing first sample, and second sample in appropriate place Input Alternative = nature of H1 (in our case, less than) Chart 11-3: Minitab Paired T-Test

Chart 11-4: Excel Paired T-Test Input Hypothesized Mean Difference = test value of (µ1µ2) ( = 0 in our case) Input data range for Variables 1 and 2 Input Alpha = value of level of significance ( = 0.05 in our case) Click t-Test: Paired Two Sample for Means Click Tools, Data Analysis Input the sample data Click OK Chart 11-4: Excel Paired T-Test