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 = .05.
b. Compute the value of r2 (percentage of variance accounted for) for these data.
To find: Whether the neurological test scores are significantly lower for the soccer player than for the swimmers using one-tailed test with
Two samples each of size 8 (for swimmers) and 5 (for soccer players). One-tailed hypothesis test using is to be performed.
Step 1: Null Hypothesis is and Alternate Hypothesis is
Step 2: For the given sample, the t-statistics will have degrees of freedom equals:
For a one-tailed test with and , the critical value (CV) is obtained from the t-table as .
Step 3: t-statistics is calculated using formula:
The values of sample means, and variance are obtained below:
Step-by-step procedure to obtain the sample mean and variance for the two groups, using the SPSS software:
Output using the SPSS software is given below:
From the SPSS output, the value sample means, and variance are
To find: The value of for the given question.
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