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Regression, Correlation and Hypothesis Testing

Regression, Correlation and Hypothesis Testing

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Question 87

An atmospheric scientist monitors the concentration of a synthetic coolant gas, C C\,C parts per trillion (ppt), in the stratosphere. The scientist believes the concentration has been growing exponentially since the start of 2005 and proposes the model

C=p×qn C = p \times q^{n} C=p×qn

where n n\,n is the number of years after 2005, and p p\,p and q q\,q are constants.

A graph of log⁡10C\log_{10} Clog10​C against n n\,n is plotted, and the resulting line of best fit has the equation:

log⁡10C=0.052n+0.86 \log_{10} C = 0.052n + 0.86 log10​C=0.052n+0.86
a.

(i) Show that, correct to three significant figures, p=7.24p = 7.24p=7.24.

(ii) Find the value of qqq, giving your answer to three significant figures.

[4]
b.

Based on the model, determine the annual percentage increase in the concentration of the gas.

[2]
c.

(i) Estimate the concentration of the gas at the start of 2025.

(ii) State one reason why this estimate might be inaccurate.

[3]
Markscheme

Regression, Correlation and Hypothesis Testing Questions

  1. A Level
  2. /Maths
  3. /Regression, Correlation and Hypothesis Testing

202 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.

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