Nine experts rated two brands of coffee in a taste-testing
experiment. A rating on a 7-point scale
(1=extremely
unpleasing,
7=extremely
pleasing) is given for each of four characteristics:
taste, aroma, richness, and acidity. The accompanying data
table contains the ratings accumulated over all four
characteristics. Complete parts (a) through (d)
below.
a.
At the
0.01
level of significance, is there evidence of a difference
in the mean ratings between the two brands?Let
μ1
be the mean rating for brand A and
μ2
be the mean rating for brand B. Determine the null and
alternative hypotheses for this test.
A.
H0:
μD≤0
(where
μD=μ1−μ2)
H1:
μD>0
B.
H0:
μD≥0
(where
μD=μ1−μ2)
H1:
μD<0
C.
H0:
μD≠0
(where
μD=μ1−μ2)
H1:
μD=0
D.
H0:
μD=0
(where
μD=μ1−μ2)
H1:
μD≠0
The test statistic is
tSTAT=nothing.
(Type an integer or a decimal. Round to two decimal places
as needed.)
The critical value(s) is(are)
nothing.
(Type integers or decimals. Round to two decimal places as
needed. Use a comma to separate answers as needed.)
Since the test statistic
▼
falls between
does not fall between
the critical value(s),
▼
do not reject
reject
H0.
There is
▼
insufficient
sufficient
evidence to conclude that the mean ratings are different between
the two brands.
b.
What assumption is necessary about the population distribution
in order to perform this test?
A.
It must be assumed that the distribution of the differences
between the measurements is approximately normal.
B.
It must be assumed that the distribution of the differences
between the measurements is skewed.
C.
It must be assumed that the distribution of the differences
between the measurements is approximately uniform.
c.
Determine the p-value in (a) and interpret its
meaning.The test statistic gives a p-value of
nothing.
(Type an integer or a decimal. Round to three decimal places
as needed.)
Interpret the meaning of the p-value in (a). Choose
the correct answer below.
A.
The p-value is the probability of obtaining a sample mean
difference less extreme than this one if the population mean
ratings for the two brands are the same.
B.
The p-value is the probability of obtaining a sample mean
difference at least as extreme as this one if the population mean
ratings for the two brands are the same.
C.
The p-value is the probability of failing to reject the
null hypothesis when it is actually false.
d.
Construct a
99%
confidence interval estimate of the difference in the mean
ratings between the two brands. Recall that
μD=μ1−μ2,
where
μ1
is the mean rating for brand A and
μ2
is the mean rating for brand B.The
99%
confidence interval estimate is
nothing≤μD≤nothing.
(Type integers or decimals. Round to two decimal places
as needed.)
Expert
Brand A
Brand B
C.C.
25
27
S.E.
25
25
E.G
17
18
B.I.
22
25
C.M.
21
24
C.N.
24
25
G.N.
26
25
R.M.
21
22
P.V.
23
24