The football coach at State University wishes to determine if there is a decreas
ID: 3325061 • Letter: T
Question
The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games. Game First half yards 109 97 99 69 147 70 Second half yards 108 80 97 69 121 64 State a conclusion using the = 0.05 level of significance. Reject Ho. The mean offensive production appears to decrease from the first hf to the second half. Do not reject Ho. There is insufficient evidence to conclude that the mean offensive production decreases from the first to the second half.Explanation / Answer
Given that,
mean(x)=98.5
standard deviation , s.d1=28.801
number(n1)=6
y(mean)=89.8333
standard deviation, s.d2 =22.5869
number(n2)=6
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =2.015
since our test is left-tailed
reject Ho, if to < -2.015
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =98.5-89.8333/sqrt((829.4976/6)+(510.16805/6))
to =0.58
| to | =0.58
critical value
the value of |t | with min (n1-1, n2-1) i.e 5 d.f is 2.015
we got |to| = 0.58 & | t | = 2.015
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:left tail - Ha : ( p < 0.58 ) = 0.70647
hence value of p0.05 < 0.70647,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: 0.58
critical value: -2.015
decision: do not reject Ho
p-value: 0.70647
we do not have enough evidence to support the claim that the mean offensive decreases first half to second half
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