an energy drink manufacturer has developed four new drink flavors and would like
ID: 3072773 • Letter: A
Question
an energy drink manufacturer has developed four new drink flavors and would like to conduct a taste test to collect data on customers' preferences. Six people were asked to sample and rate each flavor on a scale of 120. Complete parts a through c below.
Click the icon to view the flavor ratings.
what conclusions can be made about the preference for the four flavors?
a. Using =0.05 ,Click the icon to view an excerpt from a table of critical values of the studentized range.
What are the correct null and alternative hypotheses?
A.
H 0 : 1=2=3=4
H 1 : Not all the ’s are equal
B.
H 0: Not all the 's are equal
H 1 : 1=2=3=4
C.
H 0 : 1=2=3=4
H 1 : 1234
D.
H 0 : 1234
H 1: 1=2=3=4
What is the test statistic?
Fx=
(Round to two decimal places as needed.)
What is the p-value?
The p-value is .
(Round to three decimal places as needed.)
What is the correct conclusion?
A.
Reject H 0. There is insufficient evidence that any of the drinks were preferred differently.
B.
Do not reject H 0. There is insufficient evidence that any of the drinks were preferred differently.
C.
Reject H 0. There is evidence that some of the drinks were preferred differently.
D.
Do not reject H 0. There is evidence that some of the drinks were preferred differently.
b. Was blocking effective? Why or why not?
What are the correct null and alternative hypotheses?
A.
H 0 : Not all the BL 's are equal
H 1 : BL1=BL2=BL3=BL4=BL5=BL6
B.
H 0 : BL1BL2BL3BL4BL5BL6
H 1 : BL1=BL2=BL3=BL4=BL5=BL6
C.
H 0: BL1=BL2=BL3=BL4=BL5=BL6
H 1 : BL1BL2BL3BL4BL5BL6
D.
H 0: BL1=BL2=BL3=BL4=BL5=BL6
H 1: Not all the BL 's are equal
What is the test statistic?
FBL=
(Round to two decimal places as needed.)
What is the p-value?
The p-value is .
(Round to three decimal places as needed.)
What is the correct conclusion?
A.
The blocking factor was not effective because H 0 was rejected.
B.
The blocking factor was effective because H 0 was rejected.
C.
The blocking factor was effective because H 0 was not rejected.
D.
The blocking factor was not effective because H 0 was not rejected.
c. If warranted, determine which pairs of flavors were different from one another using =0.05.
Were flavors 1 and 2 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 1 and 2 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 1 and 2 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Were flavors 1 and 3 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 1 and 3 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 1 and 3 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Were flavors 1 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 1 and 4 is nothing , which means the flavors were not
preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 1 and 4 is
nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Were flavors 2 and 3 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 2 and 3 is nothing , which means the flavors were not
preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 2 and 3 is
nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Were flavors 2 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 2 and 4 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 2 and 4 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Were flavors 3 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.
A.
The absolute sample mean difference of flavors 3 and 4 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)
B.
The absolute sample mean difference of flavors 3 and 4 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
Person Flavor 1 Flavor 2 Flavor 3 Flavor 4 1 18 20 12 16 2 19 18 18 18 3 18 19 16 20 4 13 19 11 14 5 9 13 6 19 6 14 11 11 15Explanation / Answer
What are the correct null and alternative hypotheses?
A.
H 0 : 1=2=3=4
H 1 : Not all the ’s are equal
One-way ANOVA: Response versus Flavor
Source DF SS MS F P
Flavor 3 81.5 27.2 2.08 0.135
Error 20 261.5 13.1
Total 23 343.0
What is the test statistic?
Fx=2.08
(Round to two decimal places as needed.)
What is the p-value?
The p-value is 0.135.
(Round to three decimal places as needed.)
D.
The blocking factor was not effective because H 0 was not rejected.
Level N Mean StDev
Flavor 1 6 15.167 3.869
Flavor 2 6 16.667 3.724
Flavor 3 6 12.333 4.227
Flavor 4 6 17.000 2.366
Grouping Information Using Tukey Method
Flavor N Mean Grouping
Flavor 4 6 17.000 A
Flavor 2 6 16.667 A
Flavor 1 6 15.167 A
Flavor 3 6 12.333 A
Means that do not share a letter are significantly different. It is noted that since from ANOVA table, p-value>0.05, hence it is not required to perform multiple comparison.
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