# Conducting a Test of Hypothesis

Excess postexercise oxygen consumption (EPOC) describes the energy expended during the body's recovery period immediately following aerobic exercise. A journal published a study designed to investigate the effect of fitness level on the magnitude and duration of EPOC. Ten healthy young adult males volunteered for the study. Five of these were endurance trained and comprised the fit group; the other five were not engaged in any systematic training and comprised the sedentary group. Each volunteer engaged in a weight supported exercise on a cycle ergometer until 300 kilocalories were expended. The magnitude (in kilocalories) and duration (in minutes) of the EPOC of each exerciser were measured. The study results are summarized as:

VARIABLE FIT SEDENTARY p-value

(n=5) (n=5)

Magnitude (kcal) mean 12.2 12.2 0.998

Std. dev. 3.1 4.3

Duration (min) mean 16.6 20.4 0.344

Std. dev. 3.1 7.8

a.) Conduct a test of hypothesis to determine whether the true mean magnitude of EPOC differs for fit and sedentary young adult males. Use alpha=0.10

b.) The p-value for the test, part a, is given in the table. Interpret this value.

c.) Conduct a test of hypothesis to determine whether the true mean duration of EPOC differs for fit and sedentary young adult males. Use alpha=0.10

d.) The p-value for the test, part c, is given in the table. Interpret this value.

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#### Solution Preview

Excess post exercise oxygen consumption (EPOC) describes the energy expended during the body's recovery period immediately following aerobic exercise. A journal published a study designed to investigate the effect of fitness level on the magnitude and duration of EPOC. Ten healthy young adult males volunteered for the study. Five of these were endurance trained and comprised the fit group; the other five were not engaged in any systematic training and comprised the sedentary group. Each volunteer engaged in a weight supported exercise on a cycle ergometer until 300 kilocalories were expended. The magnitude (in kilocalories) and duration (in minutes) of the EPOC of each exerciser were measured. The study results are summarized as:

VARIABLE FIT SEDENTARY p-value

(n=5) (n=5)

Magnitude (kcal) mean 12.2 12.2 0.998

Std. dev. 3.1 4.3

Duration (min) mean 16.6 ...

#### Solution Summary

This Solution offers over 700 words of notes and calculations to aid you in your understanding of these questions.

Conduct the equivalent, non-parametric test of hypothesis

I am to determine whether the baseball players salary affects wins. I attached my full file below. Please let me know if i am missing an information.

According to the current Collective Bargaining Agreement, the minimum salary for a Major League Baseball player will be $390,000 in 2008 and the maximum salary in 2008 will be $27.5 million per year after ten years (2007-11 Basic Agreement, 2007). $3.15 million was the average salary of the MLB's 855 players (Kendrick, 2008). The question is, does a baseball player's salary directly affect a team's ability to win baseball games? Our paper will test this hypothesis and give the reasons behind our findings.

In order to answer the question of Major League Baseball players' salaries verses wins we will need to use a hypothesis to determine the answer. We will use a hypothesis of Ho: μ = player's salaries are equal to their performance statistics and Hı ≠ players with higher salaries do not have higher performance statistics.

Using the statistical data provided, we were able to construct two hypothesis statements that will be measured to see if salaries directly affect a team's ability to win baseball games (Lind, Marchall, & Wathen, 2008). To achieve this goal I have hypothesized that teams who have a high salary range will win more games than those teams that have players with lower salary ranges. The hypotheses to be tested are:

H0: (means of the games won are the same through out the salary scale)

H1: Not all the means are equal (at least one means is different then the others)

Data Format

ANOVA dependent variable and one factor which are seen below in table 1 and solution is seen in table 2.

Dependent variable:

Y= Total number of Wins

One Factor:

Factor A (salary of teams)

A1= $90,000,000 and over

A2= $89,999,999 to $69,000,000

A3=$68,999,999 to 48,999,999

A4=48,999,999 and below

Calculations:

Number of observation = n

Total number of observation= n1+n2+n3+n4 =n

Sample Means =

Total means =

Note that Mega stat was used for the ANOVA calculations.

Table 1

A1

90000000 + A2

$89,999,999 to

$69,000,000 A3

$68,999,999 to

48,999,999 A4

48,999,998 and

Below

95

95

88

74

95

93

99

80

83

79 67

71

69

56

90

77

89

73

83

67

71

82

81

75

100

83

88

81

79

67

Table 2.

Factor Mean n Std. Dev

A1 1=90.1

7 8.69

A2 2=80.3

8 11.09

A3 3=80.7

7 4.86

A4 4=74.0

8 11.75

Totals 81.0 30 10.83

ANOVA table

Source SS df MS F p-value

Treatment 982.21 3 327.405 3.51 .0291

Error 2,421.79 26 93.146

Total 3,404.00 29

From the calculation mega stat has determined that our test statistic (F) is 3.51.

Decision rule

To calculate the decision rule we will need to find the numerator d.f. and the denominator d.f 2.

C= 4 groups, n= 30 observations

Numerator = c-1 = 4-1 = 3

Denominator = n-c= 30-4 = 26

=2.31

Because the p value (p= .0291) is less then our level of significance which is and our calculated decision rule is less than our test statistic so we must in turn fail the hypothesis.

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