In 2012, the Detroit Tigers and the San Francisco Giants met in baseball\'s Worl
ID: 3359431 • Letter: I
Question
In 2012, the Detroit Tigers and the San Francisco Giants met in baseball's World Series. That year, the Tigers had a won-lost record of 88-74 and the Giants had a won-lost record of 94-68. The question is whether the Giants were in act the superior team based on their on lost record. So, test the claim that the true pro ortion their games wor . the Giants a ct i rti am was for the Tigers in 2012. Assume the only alternate hypothesis of interest is where the Giants are the superior team. The p-value of the hypothesis test is: Which of the following are correct conclusions? At a 1% significance level, it would appear that the Giants were in fact the superior team. At a 5% significance level, it would appear that the Giants were in fact the superior team. O At a 15% significance level, it would appear that the Giants were in fact the superior team O At a 10% significance level, it would appear that the Giants were in fact the superior team. It would seem that this 6-win difference over the course of the season is not statistically significant.Explanation / Answer
Given that,
sample one, x1 =88, n1 =162, p1= x1/n1=0.543
sample two, x2 =94, n2 =162, p2= x2/n2=0.58
null, Ho: p1 > p2
alternate, H1: p1 < p2
level of significance, = 0.15
from standard normal table,left tailed z /2 =1.036
since our test is left-tailed
reject Ho, if zo < -1.036
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.543-0.58)/sqrt((0.562*0.438(1/162+1/162))
zo =-0.672
| zo | =0.672
critical value
the value of |z | at los 0.15% is 1.036
we got |zo| =0.672 & | z | =1.036
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.6718 ) = 0.25085
hence value of p0.15 < 0.25085,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -0.672
critical value: -1.036
decision: do not reject Ho
p-value: 0.25085
option D
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