The following table records the age, aaa years, and the cumulative mileage, mmm thousand miles, for a sample of 8 used vehicles of the same model.
| Age (aaa) | 1.5 | 2.0 | 3.5 | 4.0 | 5.5 | 6.0 | 7.5 | 8.0 |
|---|---|---|---|---|---|---|---|---|
| Mileage (mmm) | 12 | 18 | 25 | 30 | 42 | 48 | 62 | 65 |
(You may use Saa=40.5S_{aa} = 40.5Saa=40.5 and Smm=2729.5S_{mm} = 2729.5Smm=2729.5)
Determine the exact value of ∑am\sum am∑am.
Find the value of SamS_{am}Sam.
Calculate the product moment correlation coefficient between aaa and mmm, giving your answer to 4 significant figures.
Interpret the value of the correlation coefficient in the context of the data.
A ninth vehicle is discovered. It is 8.5 years old and has a cumulative mileage of only 10 thousand miles.
Without further calculation, state whether the product moment correlation coefficient for the full set of nine vehicles will be higher, lower, or approximately the same as the value calculated in part (c). Give a reason for your answer.
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.