You are interested in comparing the difference in sales (in cases) of an energy

Question

You are interested in comparing the difference in sales (in cases) of an energy drink based on the type of in-store display used. To test whether there is a significant difference in sales, you randomly selected 50 days for each of the four display types (Bottom Shelf, Bottom Shelf with Neon Sign, Top Shelf, and Top Shelf with Neon Sign) to be used. Then, you collected total sales data for each of the displays. The total number of observations is 4 display types times 50 days. The partial results for ANOVA are SSTR= 1008.8 and SST= 8207.4. Use a significance level of =.05.

1. What are the correct null and alternative hypotheses?

a. H0: µ1= µ2= µ3= µ4        H1: µ1µ2µ3 µ4

b. H0: µ1µ2µ3 µ4                H1: At least one population mean is greater than all the others.

c. H0: µ1µ2µ3 µ4         H1: At least one population mean is negative.

d. H0: µ1= µ2= µ3=µ4           H1: At least one population mean is different.

e. H0: µ1<µ2<µ3 < µ4         H1: At least one sample mean is different.

2. What is the calculated value for the test statistic?

a. 14.25

b. 9.16

c. 11.61

d. 13.12

e. 8.64

3. Based on the hypothesis test, what should be your managerial conclusion?

a. The sales for all the display types are the same.

b. Sales for all the display types are different from one another.

c. The energy drink should be displayed on the top shelf.

d. The energy drink should be displayed on the top shelf with a neon sign.

e. The sales for at least one display type is different from the others.

4. After your initial ANOVA, you decide to run a Tukey test to compare the means.

What is the critical value for the Tukey test?

a. 3.88

b. 1.87

c. 11.39

d. 3.15

e. 6.14

Explanation / Answer

Ans:

1)

H0: µ1= µ2= µ3=µ4          

H1: At least one population mean is different.

Option d is correct.

2)Test statistic

F=Mean squares between groups/Mean squares within groups

dfn=4-1=3

dfd=200-4=196

SSTR=1008.8

SST=8207.4

SSTE=8207.4-1008.8=7198.6

MSR=1008.8/3=336.27

MSE=7198.6/196=36.73

F=336.27/36.73=9.16

Option b is correct.

3)Fcritical=FINV(0.05,3,196)=2.65

As,F=9.16>2.65,Reject H0.

Option e is correct.

The sales for at least one display type is different from the others.

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