A restaurant wants to test a new in-store marketing scheme in a small number of

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. 13 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 -4.8 with a standard deviation of 8.29. Using this information, they calculate a 90% confidence paired-t interval of (-8.9, -0.7). Which of the following is the best interpretation?

1) We are 90% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between -8.9 and -0.7.

2) We are 90% confident that the average difference in sales quantity between after the ad campaign to before for all restaurants is between -8.9 and -0.7.

3) The proportion of all stores that had a difference in sales between after the ad campaign to before is 90%.

4) We are 90% confident that the average difference in the sales quantity after to before of the stores sampled is between -8.9 and -0.7.

5) We are certain the the average difference in sales quantity between after the ad campaign to before for all stores is between -8.9 and -0.7.

Explanation / Answer

Answer: 1) We are 90% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between -8.9 and -0.7.

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