(a) A caf´e manager finds that the time spent of a customer in his caf´e is normally distributed with mean µ =
2 hours and standard deviation σ = 35 minutes. The caf´e launches a new coffee drink and the manager would like to see if his customers like the drink. 240 customers are interviewed and the manager finds that 56 customers like the drink.
i. Construct a 99% confidence interval for the actual proportion of customers who like the new coffee drink.
ii. The manager would like to see if the new drink can prolong customers' stay. A sample of 10 customers who ordered new drink is investigated and the length of their stays (in hours) is summarized as follows.
2.3, 2.5, 2.4, 2.3, 2, 2.5, 2.8, 1.8, 1.9, 2.3.
Construct a 95% confidence interval for the mean length of stay of customers who order the new drink.
(b) A pharmacist wants to test whether a new kind of sleeping pill would be effective to increase the hours of sleep for people who take it. A random sample of 10 persons (Group A) was given the new pills and another random sample of 13 persons (Group B) was given the old pills. Their sleep in hours were recorded as follows:
Mean Standard Deviation
Group A 8.9 0.8
Group B 8.5 0.5
Construct a 95% confidence interval for the difference of the average hours of sleep that would be obtained for the people taking the new pills over the people taking the old pills. State the assumptions made.