A meteorologist is investigating the relationship between relative humidity, hhh as a percentage, and horizontal visibility, vvv in kilometres (km), at an airport. A random sample of 12 days is selected from the previous year.
The collected data are summarised as follows:
n=12,∑h=816,∑v=156,∑v2=2240,Shh=960,Shv=−384 n = 12, \quad \sum h = 816, \quad \sum v = 156, \quad \sum v^2 = 2240, \quad S_{hh} = 960, \quad S_{hv} = -384 n=12,∑h=816,∑v=156,∑v2=2240,Shh=960,Shv=−384Calculate the product moment correlation coefficient between hhh and vvv.
Give an interpretation of your product moment correlation coefficient in the context of the study.
Find the equation of the least squares regression line of vvv on hhh in the form v=a+bhv = a + bhv=a+bh.
Give an interpretation of the value of bbb in your regression line.
(i) Use the regression line from part (c) to estimate the visibility for a day with relative humidity of 90%90\%90%.
(ii) Comment on the reliability of your answer in part (i) given that the range of relative humidities in the sample was 52%52\%52% to 84%84\%84%.
Using the regression line from part (c), the meteorologist estimates that for a humidity decrease of x%x\%x%, there will be an increase of 888 km in horizontal visibility.
Find the value of xxx.
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.