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

Where

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

1.6437 + .0777

= 1.7214

The lower confidence limit is

1.6437 - .0777

= 1.5660

So the confidence interval is

(1.5660, 1.7214)

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.