Assignment#4

Assignment#4 - StatTools Assignment#4 This assignment has...

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StatTools Assignment #4 This assignment has two parts Part I. Requirements 1. ACCESS DATA. You do not need to attach your Excel spreadsheet containing your simulated data. Since these are random samples, no two papers should contain the same results. 2. CHOOSE PROCEDURE and CALCULATE. ANOVA Summary Total Sample Size 144 Grand Mean 49.509 Pooled Std Dev 5.339 Pooled Variance 28.508 Number of Samples 4 Confidence Level 95.00% Treatment 1 Treatment 2 Treatment 3 Treatment 4 ANOVA Sample Stats Data Set #1 Data Set #1 Data Set #1 Data Set #1 Sample Size 36 36 36 36 Sample Mean 50.587 37.722 60.407 49.318 Sample Std Dev 5.254 4.417 6.398 5.097 Sample Variance 27.602 19.511 40.938 25.980 Pooling Weight 0.2500 0.2500 0.2500 0.2500 Sum of Degrees of Mean F-Ratio p-Value OneWay ANOVA Table Squares Freedom Squares Between Variation 9319.780 3 3106.593 108.973 < 0.0001 Within Variation 3991.102 140 28.508 Total Variation 13310.882 143 Difference Tukey Confidence Interval Tests of Means Lower Upper Treatment 1-Treatment 2 12.865 9.631910256 16.09814937 Treatment 1-Treatment 3 -9.819 -13.05236986 -6.586130755 Treatment 1-Treatment 4 1.269 -1.963905198 4.502333912 Treatment 2-Treatment 3 -22.684 -25.91739967 -19.45116057 Treatment 2-Treatment 4 -11.596 -14.82893501 -8.362695899 Treatment 3-Treatment 4 11.088 7.855345112 14.32158422 3. INTERPRET and COMMUNICATE CONCLUSIONS FOR THE FIRST SIMULATION. Respond to the following questions using complete sentences (exception made for the fill-in-the- blank questions). a. Are the results of the one-way ANOVA F-test what you expected? Explain why or why not using specific statistical information. Of course, to answer this question you must understand what is expected. Answering the following questions should help you understand what is expected:

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i. Do all of the populations have the same mean? µ 1 = 50.59 µ 2 = 37.72 _ µ 3 = 60.41 µ 4 = 49.32 _ ii. What are the null and alternative hypotheses? (Be sure to use proper notation) H 0 : µ 1 = µ 2 = µ 3 = µ 4 H a : not all µ i are equal to each other iii. Should you reject H 0 , or not? Are the ANOVA results what you expected? Explain and support your answer with specific statistical information. We should reject the H 0 because the p-value of .0001 is smaller than alpha of .05. Since the means of the populations used to obtain the four samples are different, it makes sense that the µ i are not equal. The ANOVA results are what I expected because the grand mean is 49.51 and the mean of the population means is 50. Also, the standard deviation for each population was 5 and the pooled standard deviation is 5.34.
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