The research department of a movie theatre chain wants to conduct a satisfaction survey at some of the theatres to determine how satisfied customers are with the theatre in which they just saw a movie and how much they spent (tickets, popcorn, etc.) Several questions will be asked but the main outcome measure of interest will be the percentage of customers who were completely satisfied and plan to return and the average amount spent. A few years ago a similar survey was conducted and it found that customers had seen an average of 5 movies at the theatre, had spent an average of $25, and 80% were completely satisfied and planned to return. The results also revealed that about two-thirds of the respondents spent anywhere from $15 to $35.
a) Determine sample size requirements. When the results are available you would like your margin of error to be plus or minus 5% for the satisfaction measure and plus or minus $1.50 for the spending value. The results should be accurate at the 95% confidence level. (Hint: Pick the sample size that satisfies all the requirements.)
b) Unfortunately, a full response is not expected. Some customers will be in a hurry after exiting the theatre and will not respond to the survey. Assuming the non-response rate is 10%, how would you adjust for this in your sampling plan?