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The question below is fill-in-the-blank. Be sure that you follow the instructions since it is computer graded. Either fill in the value you get from statcrunch OR write your answer selection exactly as it is written.

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

1) Sample Diff:  _____

2) Std. Err.:  _____

3) DF: ______

4) T-Stat:  ______

5) P-value: ______

Conclusion:

Since the P-value is_______ (low, high), we _________ (reject, fail to reject) the null hypothesis. There ________ (is/is not) sufficient evidence to suggest that the mean ACT score of non-athletes is ________(greater than, less than, different than) the mean ACT score of athletes.

Explanation / Answer

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

HA: µn-µa > 0; The mean ACT scores of non-athletes is greater than the mean score of athletes admitted to UNO.

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

1) Sample Diff: 5.89286

2) Std. Err.: 1.34814

3) DF: 21

4) T-Stat:  2.1458

5) P-value: 0.02187

Conclusion:

Since the P-value is low, we reject the null hypothesis. There is sufficient evidence to suggest that the mean ACT score of non-athletes is greater than the mean ACT score of athletes.

I have used the two sample t test

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