2. At a fast food restaurant where customers who dine inside have unlimited access to refilling their drinks, the management wants to determine how many times such a customer who buys a small drink will fill it up. They perform a survey by observing their customers for a day and find that 87 customers who bought small drinks poured themselves 143 drinks. They also determined that the standard deviation for this sample was .37 drinks. Find a 95% confidence interval for the mean number of drinks that a customer who orders a small drink will pour. Can you think of anything which could introduce bias into this test?
To find a 95% confidenct interval, we use the formula
Since we are using the sample standard deviation, and the sample size is so large, we need to use a z-score. The critical value for a 95% confidence interval is 1.960. We substitute these numbers into the formula and get
The upper concidence limit is
The lower confidence limit is
So the confidence interval is
One source of bias is the fact that the survey was conducted in one day. It might make a difference whether the particular day on which the survey was conducted was a particularly hot day or not. If the management had set the price of a small drink based on the results of a cool day, it might not remain profitable in hot weather when the customers might fill up their drinks more often.