A marine biologist is investigating the growth rates of coral fragments using a new mineral supplement. Eight coral fragments are each split into two halves; one half is treated with the supplement, and the other serves as a control. The biologist claims that the mean growth of the treated fragments is more than 1.2 mm greater than the mean growth of the control fragments over a six-month period. The recorded growths (in mm) are shown in the table below:
| Fragment | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Control (CCC) | 12.4 | 15.1 | 11.8 | 14.2 | 13.5 | 12.9 | 14.8 | 13.0 |
| Treated (TTT) | 14.5 | 16.9 | 14.3 | 17.4 | 14.9 | 15.1 | 16.7 | 15.9 |
Assuming that the differences in growth are normally distributed, test the biologist's claim at the 1% significance level. State your hypotheses clearly and show your working.
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.