Question 41
An ecologist is studying the impact of soil salinity, sss (measured in mS/cm), on the maximum growth height, hhh (measured in cm), of a particular marsh grass. Data collected from 10 different sites are plotted on a scatter diagram. For 9 of these sites, the data points exhibit a strong negative linear correlation. However, the 10th site, labeled 'Site Omega', is located at (48,82)(48, 82)(48,82), which is positioned significantly above the trend line observed in the other 9 sites.
a.[1]
State why Site Omega might be considered an outlier in this context.
b.[2]
For the other 9 sites, the following summary statistics were calculated:
Sss=648.2,Shh=392.5,Ssh=−415.8 S_{ss} = 648.2, \quad S_{hh} = 392.5, \quad S_{sh} = -415.8 Sss=648.2,Shh=392.5,Ssh=−415.8Calculate the product moment correlation coefficient, rrr, for these 9 sites. Give your answer to 3 significant figures.
c.[1]
If Site Omega were included in the calculation of the product moment correlation coefficient for all 10 sites, state what effect this would have on the value of rrr.
2.5 Statistical Hypothesis Testing Questions
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.