For each of the hand computation problems you should do the following: State the
ID: 3314698 • Letter: F
Question
For each of the hand computation problems you should do the following:
State the Null Hypothesis (as a sentence)
State the Alternative Hypothesis (as a sentence)
Show all work for each problem.
Report your conclusion (Do you retain or reject the Null? And what does that mean in terms of the problem? That is, you should write a verbal conclusion that relates back to the actual problem)
Problem 2: A marketing researcher wants to test the hypothesis that a prominently displayed logo increases preference for sports clothing. Participants are asked to rate 2 shirts. One shirt displays the Nike logo on the upper left portion of the shirt (prominently displayed). The other shirt displays the Nike logo at the bottom of the shirt. Participants rate how much they like each shirt on a scale from 1 = dislike a great deal to 7 = like a lot. Does a prominently displayed logo increase people’s preference for the shirt? Assume we used alpha = .05, a one-tailed test, and a critical value of 2.015.
Prominently Displayed 6 6 4 7 6 4
Displayed at Bottom of Shirt 4 3 4 3 3 4
Explanation / Answer
Given that,
mean(x)=5.5
standard deviation , s.d1=1.2247
number(n1)=6
y(mean)=3.5
standard deviation, s.d2 =0.5477
number(n2)=6
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =2.015
since our test is right-tailed
reject Ho, if to > 2.015
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.5-3.5/sqrt((1.49989/6)+(0.29998/6))
to =3.652
| to | =3.652
critical value
the value of |t | with min (n1-1, n2-1) i.e 5 d.f is 2.015
we got |to| = 3.65162 & | t | = 2.015
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 3.6516 ) = 0.00736
hence value of p0.05 > 0.00736,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 3.652
critical value: 2.015
decision: reject Ho
p-value: 0.00736
we have enough evidence to support the claim that prominently displayed logo increase people’s preference for the shirt
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