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Week 3Testing multiple means with ANOVAÂ

by | Sep 23, 2022 | Business & Finance /Operations Management | 0 comments

by | Sep 23, 2022 | Business & Finance /Operations Management | 0 comments

Week 3Testing multiple means with ANOVAÂ

Week 3Testing multiple means with ANOVA   For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements.  Use .05 for your significance level in making your decisions.   For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.                      1.      Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)   Set up the input table/range to use as follows:  Put all of the salary values for each grade under the appropriate grade label.     Be sure to incllude the null and alternate hypothesis along with the statistical test and result.        ABCDEFNote: Assume equal variances for all grades.                                       2.      The table and analysis below demonstrate a 2-way ANOVA with replication.  Please interpret the results.       Grade                GenderABCDEF          M242740475676 The salary values were randomly picked for each cell.    252847496677          F223441506575           243642576977                           Ho: Average salaries are equal for all grades            Ha: Average salaries are not equal for all grades            Ho: Average salaries by gender are equal             Ha: Average salaries by gender are not equal            Ho: Interaction is not significant              Ha: Interaction is significant              Perform analysis:               Anova: Two-Factor With Replication                              SUMMARYABCDEFTotal         M                Count22222212         Sum49558796122153562         Average24.527.543.5486176.546.8333         Variance0.50.524.52500.5364.515                          F                Count22222212         Sum467083107134152592         Average233541.553.5677649.3333         Variance220.524.582367.333                          Total                Count444444          Sum95125170203256305          Average23.7531.2542.550.756476.25          Variance1.5833319.58339.6666718.916731.33330.91667                                            ANOVA                Source of VariationSSdfMSFP-valueF crit          Sample37.5137.53.846150.073484.74723          Columns7841.8351568.37160.8581.5E-103.10588 Note: a number with an E after it (E9 or E-6, for example)   Interaction91.5518.31.876920.172313.10588 means we move the decimal point that number of places.   Within117129.75    For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456                  Total8087.8323                               Do we reject or not reject each of the null hypotheses?  What do your conclusions mean about the population values being tested?   Interpretation:                                                                                    3.   Using our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor?   GradeBe sure to include the null and alternate hypothesis along with the statistical test and result.       GenderABCDEF                                     Conduct and show the results of a 2-way ANOVA with replication using the completed table above.  The results should look something like those in question 2.  Interpret the results. Are the average compas for each gender (listed as sample) equal?  For each grade?  Do grade and gender interaction impact compa values?                                   4.   Pick any other variable you are interested in and do a simple 2-way ANOVA without replication.  Why did you pick this variable and what do the results show?  Variable name: Be sure to include the null and alternate hypothesis along with the statistical test and result.      GenderABCDEF          M       Hint: use mean values in the boxes.     F                                5.   Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?

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