For each of the hand computation problems you should do the following: State the
ID: 3314697 • 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 1: A marketer is hired to evaluate how consumers will respond to a newly developed energy drink. The question is whether consumers’ preference for the drink depends on its color. Half of the consumers rate an orange drink; half of them rate a clear drink. Their ratings, on a scale from 1 = dislike a great deal to 7 = like a lot, are shown below. Conduct an appropriate statistical test to determine if consumers differ in their preference for the drink based on its color. Assume we used alpha = .01, a two-tailed test, and a critical value of 3.17.
Orange: 5 6 4 5 6 4
Clear: 5 3 5 3 4 4
Explanation / Answer
Given that,
mean(x)=5
standard deviation , s.d1=0.8944
number(n1)=6
y(mean)=4
standard deviation, s.d2 =0.8944
number(n2)=6
null, Ho: u1 - u2 = 0
alternate, H1: u1 - u2 != 0
level of significance, = 0.01
from standard normal table, two tailed t /2 =4.032
since our test is two-tailed
reject Ho, if to < -4.032 OR if to > 4.032
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5-4/sqrt((0.79995/6)+(0.79995/6))
to =1.93655
| to | =1.93655
critical value
the value of |t | with min (n1-1, n2-1) i.e 5 d.f is 4.032
we got |to| = 1.93655 & | t | = 4.032
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.9366 ) = 0.111
hence value of p0.01 < 0.111,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.93655
critical value: -4.032 , 4.032
decision: do not reject Ho
p-value: 0.111
no evidence that consumers differ in their preference for the drink based on its color
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