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:
11.5,12.8,12.2,11.9,13.1,12.4,11.7,12.6,13.3,12.5 11.5, \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 12.5 11.5,12.8,12.2,11.9,13.1,12.4,11.7,12.6,13.3,12.5Carry 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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.