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. 20 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 average difference in nationwide sales quantity before the ad campaign to after (after - before) is -1 with a standard deviation of 6.05. Using this information, they calculate a 95% confidence paired-t interval of (-3.83, 1.83). Which of the following is the best interpretation? 1) We are certain the average difference in sales quantity between after the ad campaign to before for all stores is between -3.83 and 1.83.2) We are 95% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between-3.83 and 1.83.3) The proportion of all stores that had a difference in sales between after the ad campaign to before is 95%. 4) We are 95% confident that the average difference in the sales quantity after to before of the stores sampled is between -3.83 and 1.83.

Answer 1

2) We are 95% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between-3.83 and 1.83

Explanation:

The confidence interval is a estimation, from the information that the sample gives, about a parameter of the population. In this case, the difference of means.

The 95% is a measure of the confidence about the estimation about the difference of the means. There is a 95% probability that the difference of means (sales after and sales before the ad) is within the confidence interval.