Do athletes in different sports vary in terms of their readiness for college? Reported here are college entrance exam scores of fictitious random samples of college basketball and football players and male and female athletes. Is there a significant difference between groups? Write a sentence or two explaining the results.
a.
Sample 1 (Basketball Players) 
Sample 2 (Basketball Players) 






b.
Sample 1 (Males)  Sample 2 (Females) 






(a)
To find:
The significant difference in the sample statistics of the two samples.
Given:
The sample statistics is given in the table below,
Sample 1 (Basketball Players) 
Sample 2 (Football Players) 
The five step model for hypothesis testing:
Step 1. Making assumptions and meeting test requirements.
Step 2. Stating the null hypothesis.
Step 3. Selecting the sampling distribution and establishing the critical region.
Step 4. Computing test statistics.
Step 5. Making a decision and interpreting the results of the test.
Formula used:
The formula to calculate the sampling distribution of the differences in sample means is given by,
Where,
Where,
Calculation:
From the given information, the sample size of the first sample is 102, the sample size of the second sample is 117, the sample mean of the first sample is 460, the sample mean of the second sample is 442, the sample standard deviation of the first sample is 92, and the sample standard deviation of the second sample is 57.
As the significant difference in the sample statistics is to be determined, a two tailed test is applied.
Follow the steps for twosample testing as,
Step 1. Making assumptions and meeting test requirements.
Model:
Independent random samples.
Level of measurement is interval ratio.
Sampling distribution is Normal.
Step 2. Stating the null hypothesis.
The statement of the null hypothesis is that there is no significant difference in the sample s of the population. Thus, the null and the alternative hypotheses are,
Step 3. Selecting the sampling distribution and establishing the critical region.
Since, the sample size is large, Z distribution can be used.
Thus, the sampling distribution is Z distribution.
The level of significance is,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 92 for
(b)
To find:
The significant difference in the sample statistics of the two samples.
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