PRACT STAT W/ ACCESS 6MO LOOSELEAF
PRACT STAT W/ ACCESS 6MO LOOSELEAF
4th Edition
ISBN: 9781319215361
Author: BALDI
Publisher: Macmillan Higher Education
Question
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Chapter 24, Problem 24.11AYK

a.

To determine

To find out whether the standard deviations satisfy the rule of thumb for safe use of ANOVA.

a.

Expert Solution
Check Mark

Explanation of Solution

Given:

The following is the given table-

  PRACT STAT W/ ACCESS 6MO LOOSELEAF, Chapter 24, Problem 24.11AYK , additional homework tip  1

Calculation:

The largest standard deviation is 54 and smallest standard deviation is 30. The ratio of the largest standard deviation to smallest standard deviation is:

  5430=1.8

The ratio of the largest standard deviation to smallest standard deviation is less than 2. The standard deviations satisfy the rule of thumb for safe use of ANOVA.

b.

To determine

To find out whether ANOVA is safe for data.

b.

Expert Solution
Check Mark

Explanation of Solution

Given:

The following is the given table-

  PRACT STAT W/ ACCESS 6MO LOOSELEAF, Chapter 24, Problem 24.11AYK , additional homework tip  2

Calculation:

All samples are greater than 30. Sample sizes are large enough to assume that sampling distribution is normally distributed.

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

Explanation of Solution

Given:

The following is the given table-

  PRACT STAT W/ ACCESS 6MO LOOSELEAF, Chapter 24, Problem 24.11AYK , additional homework tip  3

Calculation:

Here

  k=3n=36+39+35=110

Compute combined sample mean:

  x¯=i=1knixii=1kni=36×25.1+39×8.2+35×28.7110=20.25

Compute the sum of squares:

  SSG=i=1kni(x¯ix¯)2 =36 (25.120.25) 2 +39 (8.220.25) 2 +35 (38.720.25) 2 =9008.79SSE=i=1k(ni1)si2=(361)302+(391)542+(351)372=188854

The sample size n=110 and Number of treatments k=3 .

  df1=k1=31=2

Compute mean sum of squares:

  df2=nk=1103=107

The ANOVA

Use MSEXCEL formula, to get.

The completed table is as shown below:

Since P-value is greater than 0.05, fail to reject the null hypothesis of equal means. Hence, conclude that there is insufficient evidence that the mean subcutaneous fat reductions of overweight adults who follow the three exercise programs differ.

d.

To determine

To obtain the ANNOVA f- static and P-test value also find out the evidence.

d.

Expert Solution
Check Mark

Explanation of Solution

Given:

The following is the given table-

  PRACT STAT W/ ACCESS 6MO LOOSELEAF, Chapter 24, Problem 24.11AYK , additional homework tip  4

Calculation:

The ANOVA F-static:

  F=MSGMSE=4504.41764.99

Use MSEXCEL formula, FDDIST(2.55,2,107) to get PValue=0.0827

The completed table is as shown below:

  PRACT STAT W/ ACCESS 6MO LOOSELEAF, Chapter 24, Problem 24.11AYK , additional homework tip  5

Since P-value is greater than 0.05, fail to reject the null hypothesis of equal means. Hence, conclude that there is insufficient evidence that the mean subcutaneous fat reductions of overweight adults who follow the three exercise programs differ.

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