Question

3. TV Commercials. Marketing experts for a national grocery chain claim that localized TV commercial advertisements will significantly increase the sales of La Croix sparkling water in their stores. In order to test this, a summer marketing intern from Iowa State developed a TV advertisement to show in local markets in hopes that showing commercials will result in a large increase in sales of La Croix sparkling water in stores in the following month. Suppose the intern has a random sample of 22 stores that agree to show the advertisements locally, and

Answer 1

(a)

Correct option:

True average La Criox sparking water sales by all stores in the population.

(b)

(i)

H0: Null Hypothesis: (Localized TV commercial advertisements will not significantly increase the sames of La Criox sparking water in their stores)

μ - μo <0

HA: Alternative Hypothesis: (Localized TV commercial advertisements will significantly increase the sames of La Criox sparking water in their stores) (claim)

0 < 077 - 11

(ii)

SE = s/$\sqrt{n}$

= 51.09/$\sqrt{22}$

= 10.8924

Test statistic is given by:

t = 27.43/10.8924

= 2.518

(iii)

Correct option:
P(T>t) = 0.01

(iv)

P value = 0.01 indicates strong evidence against the null hypothesis, so we reject the null hypothesis. Since P - Value = 0.01 is low, it indicates that our data are unlikely with a true null hypothesis. P value = 0.01 is the probability of obtaining an effect at least as extreme as the one in the sample data, assuming the truth of the null hypothesis.

(v)

Correct option:

overwhelming evidence against the null hypothesis.

(vi) Since p - value is very low, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that localized TV commercial advertisements will significantly increase the sames of La Criox sparking water in their stores.

(vii)

H0: Null Hypothesis: (Localized TV commercial advertisements will not significantly increase the sames of La Criox sparking water in their stores)

μ - μo <0

HA: Alternative Hypothesis: (Localized TV commercial advertisements will significantly increase the sames of La Criox sparking water in their stores) (claim)

0 < 077 - 11

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, Localized TV commercial advertisements will not significantly increase the sames of La Criox sparking water in their stores. We wrongly conclude that Localized TV commercial advertisements will significantly increase the sames of La Criox sparking water in their stores. Type I Error is committed in this situation.