Question

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 39 35 28 29 36 33 41 39 33 44 28 35 37 32 36 Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is - Select your answer - What is your conclusion? - Select your answer -

          To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature
50°C 60°C 70°C
39 35 28
29 36 33
41 39 33
44 28 35
37 32 36

Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value
Treatments
Error
Total

Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
Calculate the value of the test statistic (to 2 decimals).
The p-value is - Select your answer -
What is your conclusion?
- Select your answer -

Show more…

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature
50°C 60°C 70°C
39 35 28
29 36 33
41 39 33
44 28 35
37 32 36

Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value
Treatments
Error
Total

Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
Calculate the value of the test statistic (to 2 decimals).
The p-value is - Select your answer -
What is your conclusion?
- Select your answer -

Added by Megan H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Tanvi Garg

08/04/2023

Step 1

Calculate the mean yield for each temperature level: 50°C: $\frac{39+29+33+41+28}{5} = 34$ 60°C: $\frac{35+36+39+35+36}{5} = 36.2$ 70°C: $\frac{28+33+44+37+32}{5} = 34.8$ Show more…

Show all steps

lock

Thanks for your feedback!

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 39 35 28 29 36 33 41 39 33 44 28 35 37 32 36 Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is - Select your answer - What is your conclusion? - Select your answer -

Play audio

Feedback

Powered by NumerAI

Tanvi Garg and 60 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, the goal is to fill in this table first.

00:03 So, the first step will be to calculate the overall mean which can be calculated using sum of all the observations divided by total number of observations which will be found out to be 35.

00:20 Now, using this value you will calculate the rest of the parameters.

00:24 Second step will be to find the sum of squares for each groups.

00:29 So, sum of squares that between treatment the formula is sigma ni xi minus x bar square ok.

00:45 So, using this formula you will plug in you will take the difference between each observation and the grand mean and put in the values and you will get the answer as 70.

01:02 Then moving on for ss for error the formula will be the difference will be between the each term individual observation and the mean of that particular group.

01:17 So, this can be represented as xi xi mean square square and using this formula you will get the answer as 236 and the total will be the sum of these two which will come out to be 306.

01:41 Moving on to the degrees of freedom the degrees of freedom for the treatment is number of groups.

01:47 So, degrees of freedom for the treatment is the number of groups minus 1.

01:55 So, the number of groups are 3.

01:59 So, the degrees of freedom will be 3 minus 1.

02:03 So, 2.

02:04 Next for the error 1 for the degrees of freedom for error the formula will be total number of observations minus the number of groups...

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