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:     Complete the ANOVA table       Write the null Ho and alternative hypotheses H1   Use Descriptive statistics output to check verify normality of the 3 populations     Use Descriptive statistics output to check constant variance (equal of the population variances)

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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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