An agricultural researcher is investigating the relationship between the soil moisture content, mmm as a percentage, and the final crop yield, yyy in tonnes per hectare, across 8 test plots. The experimental results are summarized in the table below.
| Plot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Moisture mmm (%) | 15.2 | 16.8 | 18.5 | 20.4 | 21.6 | 23.2 | 25.1 | 26.8 |
| Yield yyy (tonnes) | 29.5 | 32.0 | 35.0 | 39.5 | 41.0 | 44.5 | 47.5 | 51.0 |
You may use: Smm=113.5S_{mm} = 113.5Smm=113.5 Smy=212.4S_{my} = 212.4Smy=212.4 Syy=398.0S_{yy} = 398.0Syy=398.0 ∑m=167.6\sum m = 167.6∑m=167.6 ∑y=320.0\sum y = 320.0∑y=320.0
Find the product moment correlation coefficient between yyy and mmm.
Give a reason why a linear regression model of the form y=a+bmy = a + bmy=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 yyy on mmm.
Interpret your value of bbb in context.
Use your answer to part (d) to estimate the crop yield when the soil moisture content is 22.0%22.0\%22.0%.
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.