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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.