The following data is mile times for a variety of participants in a race, divided by...
| The following data is mile times for a variety of participants in a race, divided by the participant's primary sport of interest. | ||
| Tennis | Soccer | Baseball |
| 8 | 7 | 9 |
| 7 | 6.5 | 8 |
| 7.5 | 8 | 7 |
| 7 | 7 | 8 |
| Is there evidence at .01 significance of a difference in the mean mile time for the tennis group and the rest of the participants? | ||
| Is there evidence at .01 significance of a difference in the mean mile time for the different groups? | ||
Homework Answers
Assume
population mean(u)=7, because not given in the data
given data,
sample mean, x =7.375
standard deviation, s =0.4787
number (n)=4
null, Ho: μ=7
alternate, H1: μ!=7
level of significance, α = 0.01
from standard normal table, two tailed t α/2 =5.841
since our test is two-tailed
reject Ho, if to < -5.841 OR if to > 5.841
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =7.375-7/(0.4787/sqrt(4))
to =1.567
| to | =1.567
critical value
the value of |t α| with n-1 = 3 d.f is 5.841
we got |to| =1.567 & | t α | =5.841
make decision
hence value of |to | < | t α | and here we do not reject
Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 1.5667 )
= 0.2152
hence value of p0.01 < 0.2152,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=7
alternate, H1: μ!=7
test statistic: 1.567
critical value: -5.841 , 5.841
decision: do not reject Ho
p-value: 0.2152
we do not have enough evidence to support the claim that difference
in the mean mile time for the different groups from 7.
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