Question

A corporation owns a chain of several hundred gas stations in the Atlantic provinces. The marketing director wants to test a proposed marketing campaign by running ads on some local radio stations and determining whether gas sales at a randomly selected sample of the company’s stations increase after the advertising. The following data represent gas sales in hundreds of dollars for a day before and two weeks after the advertising campaign.

Station 1 2 3 4 5 6 7

Before 485 418 434 422 423 421 446

After 504 424 465 413 418 442 420

(a) Does advertising on local radio stations increase gas sales by more than 5 hundreds of dollars for this corporation in the Atlantic provinces? Conduct appropriate analysis and make your conclusion. Use α = 0.05. (b) What assumptions, if any, need to be met satisfactorily for the inference in (a) to be valid? Are these assumptions reasonably satisfied?

Answer 1

A corporation owns a chain of several hundred gas stations in the Atlantic provinces. The marketing director wants to test a proposed marketing campaign by running ads on some local radio stations and determining whether gas sales at a randomly selected sample of the company’s stations increase after the advertising. The following data represent gas sales in hundreds of dollars for a day before and two weeks after the advertising campaign.

Station 1 2 3 4 5 6 7

Before 485 418 434 422 423 421 446

After 504 424 465 413 418 442 420

1. Does advertising on local radio stations increase gas sales by more than 5 hundreds of dollars for this corporation in the Atlantic provinces? Conduct appropriate analysis and make your conclusion. Use α = 0.05.

difference d= after-before

Upper tail test

Paired t Test
Data
Hypothesized Mean Difference	5
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	5.2857
Degrees of Freedom	6
SD	19.9392
Standard Error	7.5363
t Test Statistic	0.0379
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.4855
Do not reject the null hypothesis

Calculated t= 0.0379 < critical t value 1.9432 . Ho is not rejected.

There is not enough evidence to conclude that advertising on local radio stations increase gas sales by more than 5 hundreds of dollars for this corporation in the Atlantic provinces.

(b) What assumptions, if any, need to be met satisfactorily for the inference in (a) to be valid? Are these assumptions reasonably satisfied?

Paired t test assumptions:

The distribution of scores or difference of the paired scores are normal or approximately normal.

The paired scores are random and independent.

The random assumption is fulfilled by random selection.

Test for normality shows that Kolmogorov-Smirnov test p values is 0.150 which is > 0.05 level of significance. This shows that the normality assumption is not violated.