In an effort to determine if dogs perform certain tasks more quickly if offered
ID: 3310898 • Letter: I
Question
In an effort to determine if dogs perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of four dogs was given a reward of one piece of kibble each time they climbed a ladder. A second group of four dogs was given a reward of five pieces of kibble each time they climbed a ladder. On day 2, the groups were reversed, so the first group now got five pieces of kibble for each climb and the second group got only one piece of kibble for climbing the same ladder. The average times in seconds for each dog to climb the ladder 30 times are shown in the following table.
Do these data indicate that dogs receiving larger rewards tend to climb the ladder in less time? Use a 5% level of significance.
-What is the value of the sample test statistic? (Round three decimal places, DO NOT use excel TI-83 or TI-84 in arriving at your answer, show how you arrived at the answer manually step by step.)
-Find (or estimate) the P-value. (Round four decimal places.)
Explanation / Answer
Given that,
mean(x)=140
standard deviation , s.d1=65
number(n1)=10
y(mean)=95
standard deviation, s.d2 =110
number(n2)=22
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =140-95/sqrt((4225/10)+(12100/22))
to =1.443
| to | =1.443
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 1.833
we got |to| = 1.443 & | t | = 1.833
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.443 ) = 0.09145
hence value of p0.05 < 0.09145,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 < u2
alternate, H1: u1 > u2
test statistic: 1.443
critical value: 1.833
decision: do not reject Ho
p-value: 0.09145
we have evidence that dogs receiving larger rewards tend to climb the ladder in less time
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