Question

In: Statistics and Probability

In a completely randomized design, six experimental units were used for each of the three levels...

  1. In a completely randomized design, six experimental units were used for each of the three levels of the factor. (2 points each; 6 points total)

Source of Variation

Sum of Squares

Degrees of Freedom

Mean Square

F

Treatment

Error

432076.5

Total

675643.3

  1. Complete the ANOVA table.
  2. Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different.
  3. Use the critical value approach and α = 0.05 to test whether the population means for the three levels of the factors are the same.

Solutions

Expert Solution

Solution:

Here ,

Number of treatments k = 3

Each treatments contains 2 points

So , N = 3 * 2 = 6

degrees of freedom for treatments = k - 1 = 3 - 1 = 2

degrees of freedom for errors = n - k  = 6 - 3 = 3

degrees of freedom for Total = N - 1 = 6 - 1 = 5

Treatment sum of squares = Total sum of squares - Error sum of squares  

= 675643.3 - 432076.5

= 243566.8

Now ,

Mean square = Sum of squares/Degrees of freedom

F = Mean square(treatment) / Mean square(error)

a)

Source of Variation Sum of Squares Degrees of Freedom Mean Square F ratio
Treatment 243566.8 2 121783.4 0.8456
Error 432076.5 3 144025.5
Total 675643.3 5

b)

= 0.05

Critical value of the test

= F0.05 , df1 , df2

= F0.05,2,3

= 9.552  

(Use f distribution table)

c)

Since F = 0.8456 < F0.05,2,3 , we do not reject the null hypothesis.

We conclude that

the population means for the three levels of the factors are not significantly different.


Related Solutions

In a completely randomized design, six experimental units were used for each of the three levels...
In a completely randomized design, six experimental units were used for each of the three levels of the factor. (2 points each; 6 points total) Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatment Error 432076.5 Total 675643.3 Complete the ANOVA table. Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different. Use the critical value approach...
In a completely randomized design, seven experimental units were used for each of the five levels...
In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table (to 2 decimals, if necessary). If your answer is zero enter "0". Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total a. What hypotheses are implied in this problem : - Select your answer -Not all five treatment means are equalAll five treatment means are equalItem 9 : -...
3. In a completely randomized design, 7 experimental units were used for each of the three...
3. In a completely randomized design, 7 experimental units were used for each of the three levels of the factor. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between Treatment Error(within treatment) 432076.5 Total 675643.3 a. Complete the ANOVA table. b. Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different. c. Use the critical value approach...
7) In a completely randomized design, 4 experimental units were used for each of the seven...
7) In a completely randomized design, 4 experimental units were used for each of the seven levels of the factor. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatment 385.12 Error Total 1563.71 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatment 385.12 Error Total 1563.71 i. Complete the ANOVA table. ii. Find the F critical, and use the critical value approach at α = 0.05 to test whether the population means...
Canada Question 4 Marks) In a completely randomized design, 7 experimental units were used for each...
Canada Question 4 Marks) In a completely randomized design, 7 experimental units were used for each of the three levels of the factor. Source of Variation Between Treatment Within Treatment Total Sum of Squares 60 76 a. Complete the ANOVA table. b. Degrees of Freedom 24 Find the critical value at the 0.05 level of significance from the F table and test whether the population means are different.
In a completely randomized design, 12 experimental units were used for the first treatment, 15 for...
In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). Round p-value to four decimal places. If your answer is zero enter "0". Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,300 Error Total 1,800 At a .05 level of significance, is there a significant difference between the...
In a completely randomized design, 12 experimental units were used for the first treatment, 15 for...
In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). Round p-value to four decimal places. If your answer is zero enter "0". Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,300 Error Total 2,000 At a .05 level of significance, is there a significant difference between the...
In a completely randomized design, 11 experimental units were used for the first treatment, 19 for...
In a completely randomized design, 11 experimental units were used for the first treatment, 19 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,500 Error Total 2,100 At a 0.05 level of significance, is there a significant difference between the...
True or False 1. In a completely randomized experimental design with 10 treatments, if the sample...
True or False 1. In a completely randomized experimental design with 10 treatments, if the sample size (n) is 40 and α = 0.05, then tukey’s critical value is qα = 4.82. 2. The Chi-Square distribution is a right-skewed distribution that is dependent on two degrees of freedom (the numerator df and the denominator df).
You ask her what was the experimental unit and were the experimental units randomized. She is...
You ask her what was the experimental unit and were the experimental units randomized. She is unfamiliar with these concepts. Please explain experimental unit and the need for randomization of the experimental units to the treatment combinations to her. You decide to analyze the experiment as a 3 X 3 factorial arrangement using a completely randomized design and obtain the following ANOVA tables. Analysis of Variance Table Response: diastolic           Df Sum Sq Mean Sq F value   Pr(>F)   diet       2...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT