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.
