You want to compare if the average number of homeruns per game in the American L

Question

You want to compare if the average number of homeruns per game in the American League is the same as the average in the National League. You take a SRS of13 games on a particular day there were 7 American League games played and 6 National League games played (for you baseball fans note that we are ignoring the unnatural interleague games that are now haunting us throughout the season). The American League averaged 1.86 homeruns per game with a s.d. of 0.71. The National League averaged 1.30 per game with a s.d. of 0.67. Assuming the assumptions are met, test H0: ?1=?2 against Ha: ?1 ? ?2 at a 10% significance level. Assuming the data meets the assumptions answer the following questions:

a. What are the degrees of freedom?

b. Should you pool or unpool?

c. What is the test statistic?

d. What is the p value (range)? ( draw, label and shade the density curve regions)

e. What is your conclusion?

Explanation / Answer

Given that,
mean(x)=1.86
standard deviation , s.d1=0.71
number(n1)=7
y(mean)=1.3
standard deviation, s.d2 =0.67
number(n2)=6
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, ? = 0.1
from standard normal table, two tailed t ?/2 =2.015
since our test is two-tailed
reject Ho, if to < -2.015 OR if to > 2.015
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.86-1.3/sqrt((0.5041/7)+(0.4489/6))
to =1.4614
| to | =1.4614
critical value
the value of |t ?| with min (n1-1, n2-1) i.e 5 d.f is 2.015
we got |to| = 1.46143 & | t ? | = 2.015
make decision
hence value of |to | < | t ? | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.4614 ) = 0.204
hence value of p0.1 < 0.204,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.4614
critical value: -2.015 , 2.015
decision: do not reject Ho
p-value: 0.204

evidence to support that he average number of homeruns per game in the American League is the same as
the average in the National Leagu

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