A marine biologist is investigating the relationship between the concentration of a specific mineral, mmm in parts per million (ppm), and the annual growth rate of a particular coral species, GGG in mm per year, across 8 distinct reef locations. The observations are recorded in the table below.
| Reef Site | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Mineral Concentration mmm (ppm) | 6.0 | 12.0 | 17.0 | 21.0 | 26.0 | 30.0 | 34.0 | 38.0 |
| Growth Rate GGG (mm/year) | 4.5 | 6.7 | 8.9 | 10.1 | 12.5 | 14.1 | 15.9 | 17.3 |
You may use the following summary statistics: Smm=854.0S_{mm} = 854.0Smm=854.0 SmG=346.8S_{mG} = 346.8SmG=346.8 SGG=141.0S_{GG} = 141.0SGG=141.0 ∑m=184.0\sum m = 184.0∑m=184.0 ∑G=90.0\sum G = 90.0∑G=90.0
Find the product moment correlation coefficient between GGG and mmm.
Give a reason why a linear regression model of the form G=a+bmG = a + bmG=a+bm is appropriate for these data.
Find the value of bbb correct to 3 decimal places.
Find the equation of the regression line of GGG on mmm.
Interpret your value of bbb in context.
Use your answer to part (d) to estimate the growth rate of the coral when the mineral concentration is 25.025.025.0 ppm.
Comment on the reliability of your estimate in part (f), giving a reason.
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.