Question

The following data are from a completely randomized design. Treatment A B C 162 144 126 142 156 122 167 127 131 144 144 143 146 134 152 175 153 130 Sample mean 156 143 134 Sample variance 191.6 121.6 127.6 Compute the sum of squares between treatments. Round the intermediate calculations to whole number. Compute the mean square between treatments. Compute the sum of squares due to error. Compute the mean square due to error (to 1 decimal). Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal places. Round F to two decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total At the = .05 level of significance, test whether the means for the three treatments are equal. The p-value is: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10 What is your conclusion? Conclude that not all treatment means are equal, Do not reject the assumption that the means for all three treatments are equal

          The following data are from a completely randomized design.
Treatment
A
B
C
162
144
126
142
156
122
167
127
131
144
144
143
146
134
152
175
153
130
Sample mean
156
143
134
Sample variance
191.6
121.6
127.6
Compute the sum of squares between treatments. Round the
intermediate calculations to whole number.
Compute the mean square between treatments.
Compute the sum of squares due to error.
Compute the mean square due to error (to 1 decimal).
Set up the ANOVA table for this problem. Round all Sum of
Squares to nearest whole numbers. Round all Mean Squares to one
decimal places. Round F to two decimal
places.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
Treatments
Error
Total
At the  = .05 level of significance, test whether the
means for the three treatments are equal.
The p-value is: less than .01, between .01 and .025,
between .025 and .05, between .05 and .10, greater than
.10 
What is your conclusion?
Conclude that not all treatment means are equal, Do not reject
the assumption that the means for all three treatments are
equal

Show more…

Added by Wanda G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Tanvi Garg

08/01/2023

Step 1

Compute the sum of squares between treatments (SST). SST = n * Σ(𝑥̅_i - 𝑥̅_grand)^2, where n is the number of observations per treatment, 𝑥̅_i is the mean of treatment i, and 𝑥̅_grand is the grand mean. n = 6 (since there are 6 observations per treatment) 𝑥̅_A = Show more…

Show all steps

lock

Thanks for your feedback!

The following data are from a completely randomized design. Treatment A B C 162 144 126 142 156 122 167 127 131 144 144 143 146 134 152 175 153 130 Sample mean 156 143 134 Sample variance 191.6 121.6 127.6 Compute the sum of squares between treatments. Round the intermediate calculations to whole number. Compute the mean square between treatments. Compute the sum of squares due to error. Compute the mean square due to error (to 1 decimal). Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal places. Round F to two decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total At the = .05 level of significance, test whether the means for the three treatments are equal. The p-value is: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10 What is your conclusion? Conclude that not all treatment means are equal, Do not reject the assumption that the means for all three treatments are equal

Play audio

Feedback

Powered by NumerAI

Tanvi Garg and 55 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 So, this is what the table is given and treatment a, b and c these are the observations in the second column and their corresponding mean and variance.

00:12 Mean for each treatment is labeled as mu a, b and c and used like that thereof.

00:18 So, the first step is to find the sum of squares between the groups.

00:23 For this we will need to find the mu mean overall.

00:26 So, that is labeled as mu.

00:27 For this you will take the sum of all the observations divided by the total number of observations that is 18.

00:35 On solving you will get the answer 144 .3.

00:39 For calculating the sum of squares in between the groups you will use this formula where you will take the difference of each term with the overall mean and you will take the summation of all the team all the terms and finally the answer will come out to be 1468.

00:59 Next step is to find the mean square between treatments.

01:03 Here first we will need the degrees of freedom.

01:06 Degrees of freedom comes out to be 2 between treatment because there are 3 treatments in total and degrees of freedom is n minus 1.

01:17 So 2 and we will find the mean square between the treatments by dividing the sum of squares between the groups divided by the degree of freedom which will come out to be 734.

01:30 Moving on next step is to find the sum of square due to error.

01:35 For this one you will take the difference in each term.

01:40 So xi is each term and subtract their corresponding treatments mean.

01:47 So mu a, mu b or mu c depending on which group you take the term from and take their sum total summation...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later