A logistics company claims that the average delivery time for local parcels is 12 hours. A manager suspects that recent changes in the sorting process have altered this mean delivery time. A random sample of 10 parcels is monitored, and their delivery times in hours are recorded as follows:
11.5,12.8,12.2,11.9,13.1,12.4,11.7,12.6,13.3,12.511.5, \quad 12.8, \quad 12.2, \quad 11.9, \quad 13.1, \quad 12.4, \quad 11.7, \quad 12.6, \quad 13.3, \quad 12.511.5,12.8,12.2,11.9,13.1,12.4,11.7,12.6,13.3,12.5
Carry out a hypothesis test at the 5% significance level to investigate whether the mean delivery time has changed. You may assume that delivery times are normally distributed with a standard deviation of 0.6 hours.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.