Question

A restaurant wants to test a new in-store marketing scheme in a small number of stores before rolling it out nationwide. The new ad promotes a premium drink that they want to increase the sales of. 18 locations are chosen at random and the number of drinks sold are recorded for 2 months before the new ad campaign and 2 months after. The 90% confidence interval to estimate the true average difference in nationwide sales quantity before the ad campaign and after is (5.11, 20.14). Which of the following is the appropriate conclusion? The differences were calculated as (after ad campaign - before ad campaign).

options:

1) We are 90% confident that the average difference in sales quantity for all stores is negative, with the higher sales coming after the ad campaign.

2) We are 90% confident that the average difference in sales quantity for all stores is positive, with the higher sales coming after the ad campaign.

3) We are 90% confident that the average difference in sales quantity for all stores is positive, with the higher sales being before the ad campaign.

4) There is not a significant difference between the average sales quantity before or after the ad campaign.

5) We are 90% confident that the average difference in sales quantity for all stores is negative, with the higher sales being before the ad campaign.

Answer 1

Given,

The 90% confidence interval to estimate the true average difference in nationwide sales quantity before the ad campaign and after is (5.11, 20.14);

i.e Lower Confidence Limit :LCL = 5.11 and Upper Confidence limit: UCL= 20.14

That means the average difference in sales quantity for all stores is between 5.11 and 20.14

i.e We are 90% confident that the average difference in sales quantity for all stores is positive

The differences were calculated as (after ad campaign - before ad campaign).

i.e

Sales after ad campaign - Sales before ad campaign > 0

Sales after ad campaign > Sales before ad campaign i.e  higher sales coming after the ad campaign  

Therefore , the answer

2) We are 90% confident that the average difference in sales quantity for all stores is positive, with the higher sales coming after the ad campaign.