Question

6. A randomized block analysis was performed to examine whether the color of an energy drink (e.g., red, green, blue, purple) has an effect on the sales of the energy drink. Because the type of store (e.g., convenience, grocery, and discount) where the drink is sold could have an effect on sales the analyst decided to control for store differences by blocking on stores (the analyst believes the stores could be a nuisance in the analysis). Three blocks were used in the analysis. The results of the hypothesis tests for whether blocking is effective or not resulted in an F calculated of 1.76 which had a p-value of 0.206. If the analyst wants to control for the probability of a Type 1 Error to be no more than 0.05 (α=0.05), then the analyst would

a. Reject the null hypothesis and conclude that there is a store effect (blocking was effective)

b. Not reject the null hypothesis and conclude that there is no store effect (blocking was not effective)

c. Reject the null hypothesis and conclude that there is no effect due to stores (blocking was not necessary)

d. Not reject the null hypothesis and conclude that there is a store effect (blocking was necessary)

Answer 1

Solution: For the given question, a randomized block analysis was performed to examine whether the color of an energy drink has an effect on the sales of the energy drink. For this, three blocks were used in the analysis. The block effect used is the stores.The result obtaind shows that F calculated of 1.76 which had a p-value of 0.206.

If the null hypothesis is rejected we conclude that there is an effect of blocking, i.e. , there is a store effect.

In Statistics, p-value is the probability of obtaining results as extreme as the observed results of a statistical hypithesis test, assuming that the null hypothesis is correct. We reject the null hypotesis is p-value is less than the level of significance, α, here α=0.05.

It is given that the p-value is obtained to be 0.206. Where α = 0.05. Thus, p-value > α.

Hence we decide that we should not reject the null hypothesis and conclude that there is no store effect (blocking was not effective).

Thus, Option (b) is correct.