Chapter 10, Problem 23P

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

# Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the study, neurological tests were administered to mature soccer players and swimmers and the results indicated significant differences. In a similar study, a researcher obtained the following data.a. Are the neurological test scores significantly lower for the soccer players than for the swimmers in the control group? Use a one-tailed test with α = .05.b. Compute the value of r2 (percentage of variance accounted for) for these data.

a.

To determine

To find: Whether the neurological test scores are significantly lower for the soccer player than for the swimmers using one-tailed test with α=0.05

Explanation

Given info:

Two samples each of size 8 (for swimmers) and 5 (for soccer players). One-tailed hypothesis test using α=0.05 is to be performed.

Calculations:

Step 1: Null Hypothesis is H0:μ1μ2 and Alternate Hypothesis is H1:μ1>μ2

Step 2: For the given sample, the t-statistics will have degrees of freedom equals:

df=n1+n22=8+52=11

For a one-tailed test with α=0.05 and df=11, the critical value (CV) is obtained from the t-table as t=1.796.

Step 3: t-statistics is calculated using formula:

t=(M1M2)(μ1μ2)sM1M2

The values of sample means, and variance are obtained below:

Software procedure:

Step-by-step procedure to obtain the sample mean and variance for the two groups, using the SPSS software:

• Go to Variable View> Enter the name of the variable as Swimmers and Soccer.
• Go to Data View>Enter the values of Swimmers and Soccer.
• Choose Analyze > Descriptive Statistics> choose Descriptive.
• Select Swimmers and Soccer and move it under variable(s)> Choose Options> Select Mean , Std. Deviation and Variance
• Choose Continue> choose OK.

Output using the SPSS software is given below:

From the SPSS output, the value sample means, and variance are

M1=9,M2=6,s12=6.28,s22=6 Respectively.

Pooled variance:

sp2=(df1)s12+(df2)s22df1+df2=(7)6

b.

To determine

To find: The value of r2 for the given question.

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