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.
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.