A marine biologist believes that adult green sea turtles in the Coral Sea have a mean shell length that is more than 15 cm greater than the mean shell length of those in the Tasman Sea.
A random sample of 80 turtles from the Coral Sea was found to have a mean shell length of 126.2 cm with a standard deviation of 11.5 cm.
A random sample of 100 turtles from the Tasman Sea was found to have a mean shell length of 108.4 cm with a standard deviation of 9.8 cm.
Stating your hypotheses clearly, test the biologist's claim at the 5% level of significance.
Explain whether it was necessary to assume that the shell lengths of the turtles are normally distributed for this test to be valid.
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.