The daily rainfall in a certain region during the monsoon season is modeled by a normal distribution with a mean of 22 mm and a standard deviation of 6.8 mm. A researcher believes that recent climate shifts have caused the mean daily rainfall to increase. A random sample of 40 days during the current monsoon season is taken, and the mean daily rainfall is found to be 24.5 mm. Carry out a hypothesis test at the 5% significance level to investigate the researcher's claim.
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.