Question

The waiting time for Restaurant DD to deliver your food when ordering online is normally distributed. A random sample of 6 days in the last month indicated the following waiting times (in minutes) 41 33 42 38 37 35

(a) [1 mark] Determine the sample mean and standard deviation. You may use your calculator, so no justification is needed.

(b) [1 mark] What critical value would you use to construct a 95% confidence interval? Explain your choice.

(c) [2 marks] Construct a 95% confidence interval on the waiting time for the food delivery from Restaurant DD.

(d) [2 marks] Using your answer from (c), is it likely that the true mean waiting time is 33 minutes? Why or why not?

(e) [2 marks] Is it possible that the true mean waiting time is 33 minutes? If the true mean waiting time was 33 minutes, then what would you say about this sample

Answer 1

Solution:

Meanstandard deviation (s) =

b) confidance interval = 95%

Using t test :

df = n - 1 = 6-1 = 5

Critical value at 95% ()= 2.571

c)margin of error (E) =

Confidence interval =  

lower limit = 37.67 - 3.61 = 34.06

Upper limit = 37.67 + 3.61= 41.28

d) the mean waiting time of 33 minutes is not likely to be true mean

Because value 33 is less then 34.06, which is outside the interval.