9.8 In a study of 10 new producers of iron supplements, nine contrasts in the mean iron level in the supplements were constructed by the quality control department for comparing various characteristics of the producers.a. In order to achieve an experimentwise error rate of .05, what value should be selected for the value of aI?b. What is the critical value for the F statistic for testing the nine contrasts if there were six samples of the supplement taken from each of the 10 producers?

Question
Asked Mar 7, 2019

9.8 

In a study of 10 new producers of iron supplements, nine contrasts in the mean iron level in the supplements were constructed by the quality control department for comparing various characteristics of the producers.

a. In order to achieve an experimentwise error rate of .05, what value should be selected for the value of aI?

b. What is the critical value for the F statistic for testing the nine contrasts if there were six samples of the supplement taken from each of the 10 producers?

check_circle

Expert Answer

Step 1

Part (a):

The experiment-wise error rate is the probability of committing one or more Type I error, while making several comparisons in an experiment.

Suppose an experiment is performed with j contrasts, with αe denoting the experiment-wise error rate. If α1 denotes the comparison-wise error rate, then the relationship between the two error rates is αe = 1– (1 – α1)j.

In case the contrasts are independent of each other (orthogonal), the above relationship holds. In case the contrasts are not independent, αe ≤ 1– (1 – α1)j.

In this case, j = 9, αe = 0.05. Thus, the value of α1 is calculated as follows:

fullscreen
Step 2

Part (b):

The F-statistic is used here for pairwise comparisons. Thus, the numerator degrees of freedom would always be 1.

If there are k treatments each with n observations, then the denominator degrees of freedom of the F-statistic is (nkk).

Now, 6 samples are taken from each of 10 producers. Thus, total sample size is nk = 60. Here, k = 10. Thus, the denominator degrees of freedom is 60 – 10 = 50.

The level of significance for the critical ...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Douglas is a farmer who believes that his cow produces an average of 7 gallons of milk per day. To t...

A: The aim is to find the range of p-value.

question_answer

Q: Is the national crime rate really going down? Some sociologists say yes! They say that the reason fo...

A: 1) Computation of test statistic:Here, the appropriate test to check whether the population proporti...

question_answer

Q: In a survey of 4061 ​adults, 738 say they have seen a ghost. Construct a​ 99% confidence interval fo...

A: In this question, it has been given that 738 people out of 4061 people have seen the ghost, we have ...

question_answer

Q: Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annu...

A: (a)Using the provided data, the sample mean can be calculated using Excel function “AVERAGE()”.Enter...

question_answer

Q: How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in te...

A: (a)Using the provided data, the sample mean and standard deviation can be calculated using Excel fun...

question_answer

Q: 15.) The age in years of 11 children and the number of words in their vocabulary is given below:    ...

A: The equation of the regression line is:

question_answer

Q: Let S be a given sample space and let E and F be two events that have no common outcome and their un...

A: Probability of two events:It is given that E and F are the two events in sample space, S. The probab...

question_answer

Q: D, E, F

A: In this question, we have the data for two groups and we have to find the inference about  the popul...

question_answer

Q: Are there ever any circumstances when a correlation such as Pearson's r can be interpreted as eviden...

A: Correlation between any two variables tell us the linear association meaning that one variable rise ...