Question

A marketing researcher analyzing the fast-food industry noticed the following: The average amount spent at a fast- food restaurant in California was $3.30, with a standard deviation of $0.40. Yet in Georgia, the average amount spent at a fast-food restaurant was $3.25, with a standard deviation of $0.10. What do these statistics tell you about fast-food consumption patterns in these two states?

Describe how a pilot study can help a researcher determine the appropriate sample size to use in the full study.

Answer 1

For california; average spend at a restaurant is $3.30, but the standard deviation is 0.40; which means the range of spend is higher, on average say $2.90 to $3.70. This means that the people spend in high deviation, good amount of people spend around 3, and good amount of people spend in higher ranges around $3.6. An assumption can be stated here that maybe the income disparity between the people is high in california. hence some spend higher on food, and some in lower ranges. There are a few in middle income group, who spend on average

On the other hand, in Georgira, average spend is $3.25; while the standard deviation is just $0.10; which means a large number of people spend in the average range of $3.15 to $3.35. This means that a lot of people spend in average, and there are very few people spending say near $4; and very few who spend in lower ranges say near $2.5. This can lead to an assumption that income disparity in Georgia is less than the income disparity in California. More number of people in Georgia are earning at same levels, where as there is a wider gap between average earnings in California

How does a pilot study help a researcher determine the appropriate sample size -

A research has certain hypothesis, around which a researcher carries out his/her study. The findings of the study somewhat lead to closely accepting hypothesis, or rejecting. Pilot study helps in-

1. Determing errors like alpha errors and Beta errors, if these errors are way out of ranges, this means the sample size is not right, or sample population is not right

2. Huge standard deviation, means the size maybe too small, causing huge disparity in results, this should help you approximate the right sample size.

3. Averages of the sample size may result in huge deviation from the expectation of your research, this again helps you estimate the right sample size.

Above are a few reasons how pilot study can help you pick up the right sample size. If you have any doubts regarding the answer, or want any calrifications on any of the points, or want some more points, please comment, I would like to resolve any of your queries as soon as possible. Thank You