A cheerleading squad received a mean rating (out of 100 possible points) of 71 ±
ID: 3180353 • Letter: A
Question
A cheerleading squad received a mean rating (out of 100 possible points) of
71 ± 11 ( ± )
in competitions over the previous three seasons. The same cheerleading squad performed in 16 local competitions this season with a mean rating equal to 74 in competitions. Suppose we conduct a one-independent sample z-test to determine whether mean ratings increased this season (compared to the previous three seasons) at a 0.05 level of significance.
(a) State the value of the test statistic. (Round your answer to two decimal places.
Compute effect size using Cohen's d. (Round your answer to two decimal places.
Explanation / Answer
Given that,
population mean(u)=71
standard deviation, =11
sample mean, x =74
number (n)=16
null, Ho: <71
alternate, H1: >71
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 74-71/(11/sqrt(16)
zo = 1.09091
| zo | = 1.09091
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.09091 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : right tail - ha : ( p > 1.09091 ) = 0.13766
hence value of p0.05 < 0.13766, here we do not reject Ho
ANSWERS
---------------
null, Ho: <71
alternate, H1: >71
test statistic: 1.09091
critical value: 1.645
decision: do not reject Ho
p-value: 0.13766
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