Question

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A cafe manager finds that the time spent of a customer in his cafe 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. [4 marks]

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.

Answer 1

(i)

(ii)

Sample mean = (2.3+2.5+2.4+2.3+2+2.5+2.8+1.8+1.9+2.3)/10 = 2.28