Question

The mean height of 50 male students who showed above-average participation in college
athletics was 68.2 inches with a standard deviation of 2.5 inches, while 50 male students
who showed no interest in such participation had a mean height of 67.5 inches with a
standard deviation of 2.8 inches.
(a) Test the hypothesis that male students who participate in college athletics are taller
than other male students.
(b) What is the P value of the test?

Answer 1

We have given that→

##)The mean height of 50 male students who showed above-average participation in college athletics was 68.2 inches with a standard deviation of 2.5 inches

This imply that

Sample size (n1)=50

Sample mean (x1bar)=68.2

Standard deviation (s1)=2.5

##)

50 male students
who showed no interest in such participation had a mean height of 67.5 inches with a standard deviation of 2.8 inches.

This means→

n2=50

S2=2.8

X2bar=67.5

Setting up hypothesis:

Ho: u1=u2

H1:u1>u2

Test statistic:

Z= (x1bar-x2bar)/√(s1²/n1+s2²/n2)

Z=(68.2-67.5)/√(2.5²/50+2.8²/50)

=1.3186439≈1.3186(ans)

Pvalue= prob(z>1.3186)

=1 - Prob(z<1.3186)=1-0.9036

=0.0964

≈0.0964(ans)

Now, since p value is greater than the level of significance 0.05

We fail to Reject Null hypothesis.

Conclusion:

We have insufficient evidence to claim that male students who participate in college athletics are taller
than other male students.

Thanks!

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