an energy drink manufacturer has developed four new drinkflavors and would like to conduct a taste test to collect data oncustomers' preferences. Six people were asked to sample and rateeach flavor on a scale of 1−20. Complete parts a through cbelow.
Click the icon to view the flavor ratings.
| 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 | 15 |
what conclusions can be made about the preference forthe four flavors?
a. Usingα=0.05,Click the icon to view an excerpt from atable of critical values of the studentized range.
What are the correct null and alternativehypotheses?
A.
H 0 : μ1=μ2=μ3=μ4
H 1 : Not all the μ’s are equal
B.
H 0: Not all the μ 's are equal
H 1 : μ1=μ2=μ3=μ4
C.
H 0 : μ1=μ2=μ3=μ4
H 1 : μ1≠μ2≠μ3≠μ4
D.
H 0 : μ1≠μ2≠μ3≠μ4
H 1: μ1=μ2=μ3=μ4
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 thedrinks were preferred differently.
B.
Do not reject H 0. There is insufficient evidence that any ofthe drinks were preferred differently.
C.
Reject H 0. There is evidence that some of the drinks werepreferred differently.
D.
Do not reject H 0. There is evidence that some of the drinkswere preferred differently.
b. Was blocking effective? Why or whynot?
What are the correct null and alternativehypotheses?
A.
H 0 : Not all the μBL 's are equal
H 1 : μBL1=μBL2=μBL3=μBL4=μBL5=μBL6
B.
H 0 : μBL1≠μBL2≠μBL3≠μBL4≠μBL5≠μBL6
H 1 : μBL1=μBL2=μBL3=μBL4=μBL5=μBL6
C.
H 0: μBL1=μBL2=μBL3=μBL4=μBL5=μBL6
H 1 : μBL1≠μBL2≠μBL3≠μBL4≠μBL5≠μBL6
D.
H 0: μBL1=μBL2=μBL3=μBL4=μBL5=μBL6
H 1: Not all the μBL '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 wasrejected.
B.
The blocking factor was effective because H 0 was rejected.
C.
The blocking factor was effective because H 0 was notrejected.
D.
The blocking factor was not effective because H 0 was notrejected.
c. If warranted, determine which pairsof flavors were different from one another usingα=0.05.
Were flavors 1 and 2 preferred differently? Choose thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 1 and 2 isnothing , 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 isnothing , 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 thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 1 and 3 isnothing , 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 isnothing , 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 thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 1 and 4 isnothing , which means the flavors were not
preferred differently. (Round to two decimal places asneeded.)
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 thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 2 and 3 isnothing , which means the flavors were not
preferred differently. (Round to two decimal places asneeded.)
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 thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 2 and 4 isnothing , 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 isnothing , 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 thecorrect answer below and, if necessary, fill in any answer boxes inyour choice.
A.
The absolute sample mean difference of flavors 3 and 4 isnothing , 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 isnothing , which means the flavors were not preferred differently.(Round to two decimal places as needed.)
C.
Multiple comparisons are not warranted.
