# Problem4 (Use the Formula shee

Problem4 (Use the Formula sheet and the Tables to answer this question, You should not use Mega-Stat)

The output below represents Descriptive statistics and ANOVA a random samples of six students in 3 schools produced the following GMAT scores

To test the claim that there are significant differences between the averages of 3 GMAT populations scores

 Descriptive statistics School 1 School 2 School 3 count 6 6 6 mean 646.67 606.67 523.33 sample variance 2,266.67 4,746.67 1,266.67 sample standard deviation 47.61 68.90 35.59 minimum 580 510 490 maximum 710 700 590 range 130 190 100 normal curve GOF p-value .4142 .4142 .1573 chi-square(df=1) 0.67 0.67 2.00 E 1.50 1.50 1.50 O(-0.67) 1 2 1 O(+0.00) 2 1 3 O(+0.67) 1 2 1 O(inf.) 2 1 1 One factor ANOVA Mean n Std. Dev 646.7 6 47.61 School 1 606.7 6 68.90 School 2 523.3 6 35.59 School 3 592.2 18 72.32 Total ANOVA table Source SS df MS F p-value Treatment 47,511.11 2 ———- —— .0032 Error 41,400.00 —— 2,760.000 Total 88,911.11 17 Tukey simultaneous comparison t-values (d.f. = 15) School 3 School 2 School 1 523.3 606.7 646.7 School 3 523.3 School 2 606.7 2.75 School 1 646.7 4.07 1.32 critical values for experimentwise error rate: 0.05 2.60 0.01 3.42

Use the above output to answer the following questions:

1. Complete the ANOVA table

1. Write the null Ho and alternative hypotheses H1

1. Use Descriptive statistics output to check verify normality of the 3 populations

1. Use Descriptive statistics output to check constant variance (equal of the population variances)

1. Use critical value method, to test the claim at a = 05,

1. Use P-value method, to test the claim at a = 05

1. If differences exists. Use the Tukey test to find which pairs of means are significantly different? at a = 05

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