EBK PRACTICE OF STATISTICS IN THE LIFE
EBK PRACTICE OF STATISTICS IN THE LIFE
4th Edition
ISBN: 9781319067496
Author: BALDI
Publisher: VST
Question
Book Icon
Chapter 24, Problem 24.10AYK

(a)

To determine

To explain do the standard deviations satisfy the rule of thumb for safe use of ANOVA.

(a)

Expert Solution
Check Mark

Answer to Problem 24.10AYK

Yes, the standard deviations satisfy the rule of thumb for safe use of ANOVA.

Explanation of Solution

In the question, it is given that a study examined the impact of exercise type on visceral and subcutaneous fat. Overweight but otherwise disease free adults were assigned to three exercise regiments for eight months. The study report contains the information given in the question about the visceral fat reduction achieved by the subjects in each group. Thus, the standard deviation rule of thumb is that the largest sample standard deviation is no more than twice as large as the smallest standard deviation. Thus, the standard deviation is already given in the question, so let us find the ratio as:

  Largest sSmallest s=3419=1.79

Thus, the standard deviations satisfy the rule of thumb for safe use of ANOVA.

(b)

To determine

To explain why ANOVA is nonetheless safe for these data.

(b)

Expert Solution
Check Mark

Explanation of Solution

In the question, it is given that a study examined the impact of exercise type on visceral and subcutaneous fat. Overweight but otherwise disease free adults were assigned to three exercise regiments for eight months. The study report contains the information given in the question about the visceral fat reduction achieved by the subjects in each group. Thus, the standard deviation rule of thumb is that the largest sample standard deviation is no more than twice as large as the smallest standard deviation. And the standard deviations satisfy the rule of thumb for safe use of ANOVA. The report does not provide the distributions of visceral fat reduction. But ANOVA nonetheless safe for these data because as we look at the means and standard deviations given then we can assume that they are approximately normally distributed and also all the other conditions are satisfied.

(c)

To determine

To calculate the overall mean response x¯ , the mean square for groups (MSG) and the mean square for error (MSE).

(c)

Expert Solution
Check Mark

Answer to Problem 24.10AYK

The overall mean response x¯ is 8.96 , the mean square for groups (MSG) is 2231.226 and the mean square for error (MSE) is 852.3738 .

Explanation of Solution

In the question, it is given that a study examined the impact of exercise type on visceral and subcutaneous fat. Overweight but otherwise disease free adults were assigned to three exercise regiments for eight months. The study report contains the information given in the question about the visceral fat reduction achieved by the subjects in each group. Thus, the standard deviation rule of thumb is that the largest sample standard deviation is no more than twice as large as the smallest standard deviation. And the standard deviations satisfy the rule of thumb for safe use of ANOVA. Thus, the overall mean response x¯ , the mean square for groups (MSG) and the mean square for error (MSE) can be calculated as:

The calculations are as:

    Treatmentnx barn*x barn*(x-x total)^2s^2SS=(n-1)*s^2
    13615.9=BO50*BP50=BO50*(BP50-$BP$54)^2=34^2=(BO50-1)*BS50
    2390.8=BO51*BP51=BO51*(BP51-$BP$54)^2=19^2=(BO51-1)*BS51
    33510.9=BO52*BP52=BO52*(BP52-$BP$54)^2=33^2=(BO52-1)*BS52
    Total=SUM(BO50:BO52)=SUM(BQ50:BQ52)=SUM(BR50:BR52)=SUM(BT50:BT52)
    Grand mean=BQ53/BO53SStrSSE
    Source of variationdfSSMSF
    Groups=3-14462.452=BP60/BO60=BQ60/BQ61
    Error=110-391204=BP61/BO61
    Total=BO60+BO61=SUM(BP60:BP61)

The result will be as:

    Treatmentnx barn*x barn*(x-x total)^2s^2SS=(n-1)*s^2
    13615.9572.41736.162115640460
    2390.831.22593.94636113718
    33510.9381.5132.344108937026
    Total110985.14462.45291204
    Grand mean8.955455SStrSSE
    Source of variationdfSSMSF
    Groups24462.4522231.2262.617661
    Error10791204852.3738
    Total10995666.45

Thus, the overall mean response x¯ is 8.96 , the mean square for groups (MSG) is 2231.226 and the mean square for error (MSE) is 852.3738 .

(d)

To determine

To obtain the ANOVA F statistic and the test P-value and explain is there evidence that the mean visceral fat reduction in overweight adults depends on which three exercise programs they follow.

(d)

Expert Solution
Check Mark

Answer to Problem 24.10AYK

The ANOVA F statistic is 2.62 and the test P-valueis between 0.05<P<0.10 and there is no evidence that the mean visceral fat reduction in overweight adults depends on which three exercise programs they follow.

Explanation of Solution

In the question, it is given that a study examined the impact of exercise type on visceral and subcutaneous fat. Overweight but otherwise disease free adults were assigned to three exercise regiments for eight months. The study report contains the information given in the question about the visceral fat reduction achieved by the subjects in each group. Thus, the standard deviation rule of thumb is that the largest sample standard deviation is no more than twice as large as the smallest standard deviation. And the standard deviations satisfy the rule of thumb for safe use of ANOVA. And from part (d) we have the ANOVA table as:

    Source of variationdfSSMSF
    Groups24462.4522231.2262.617661
    Error10791204852.3738
    Total10995666.45

Thus, the P-value is 0.05<P<0.10 and as we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  P>0.05Fail to Reject H0

Thus, we do not have sufficient evidence to conclude that the mean visceral fat reduction in overweight adults depends on which three exercise programs they follow.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman