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 1−20. Complete parts a through c below.

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 for the four flavors?
a. Using α=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 : 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 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 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 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 α=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.

Answer 1

What are the correct null and alternative hypotheses?

A.

H 0 : μ1=μ2=μ3=μ4

H 1 : Not all the μ’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.