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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 201

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.

Scatter diagram of maximum growth height against soil salinity, showing nine negatively correlated sites with a trend line and Site Omega at (48, 82) well above the line.

a.

State why Site Omega might be considered an outlier in this context.

[1]
b.

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​=−415.8

Calculate the product moment correlation coefficient, rrr, for these 9 sites. Give your answer to 3 significant figures.

[2]
c.

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.

[1]
Markscheme

2.5 Statistical Hypothesis Testing Questions

  1. A Level
  2. /Maths
  3. /2.5 Statistical Hypothesis Testing

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.

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