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Twenty-three students from Bellevue East High school were admitted to UNO last term. Of those, 7 were offered athletic scholarships. The ACT scores of all 23 students is listed. Do you feel that UNO admits students with lower ACT scores if they are also athletes? Test the appropriate hypothesis and state your conclusion. Assume the conditions have been met.  Include the following:

Hypotheses:

H0: µn-µa=0; There is no difference in the mean ACT scores of athletes and non-athletes admitted to UNO

HA: µn-µa  (<, >, non equal to) 0; The mean ACT scores of non-athletes is  (greater than, less than, different than) the mean score of athletes admitted to UNO.

Calculations: Type each value EXACTLY as they are given in StatCrunch unless otherwise indicated

Sample Diff:

Std. Err.:

DF:

T-Stat:

P-value:

Conclusion:

Explanation / Answer

HA: µn-µa > 0

The mean ACT scores of non - athelete is greater than the mean score of atheletes admitted to UNO.

The statcrunch output for this problem is:

Two sample T hypothesis test:
1 : Mean of Non-Athletes
2 : Mean of Athletes
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 > 0
(with pooled variances)

Hypothesis test results:

Hence,

Sample diff. = 2.8928571

Std. Err. = 1.3481397

DF = 21

T-Stat = 2.1458141

p - Value = 0.0219

Conclusion: low; reject; is; greater than

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