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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.