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.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.