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2.5 Data presentation and interpretation

2.5 Data presentation and interpretation

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Question 63

A chemical engineer is investigating the relationship between the concentration of a specific catalyst, CCC (grams per liter), and the resulting reaction rate, RRR (moles per second). The least squares regression line of R R\,R on C C\,C is found to be:

R=18.00−0.750C R = 18.00 - 0.750C R=18.00−0.750C

The following summary statistics were recorded from a sample of 15 trials:

∑R=180.0,∑R2=2460,∑C2=1380,n=15 \sum R = 180.0, \quad \sum R^2 = 2460, \quad \sum C^2 = 1380, \quad n = 15 ∑R=180.0,∑R2=2460,∑C2=1380,n=15
a.

Show that SRR=300S_{RR} = 300SRR​=300.

[1]
b.

Find SCCS_{CC}SCC​.

[3]
c.

Find the product moment correlation coefficient between C C\,C and RRR.

[2]
d.

One lab assistant claims that when the catalyst concentration is 20 g/L, the reaction rate will be under 4.0 mol/s.

Explain how the lab assistant could have reached this conclusion.

[1]
e.

Another researcher uses the formula

range=mean±2.2×standard deviation \text{range} = \text{mean} \pm 2.2 \times \text{standard deviation} range=mean±2.2×standard deviation

to estimate the interval of typical values for CCC.

Find estimates for the minimum and maximum values of C C\,C in these data using this formula.

[3]
f.

Comment, giving a reason, on the reliability of the lab assistant's claim in part (d).

[2]
g.

The engineer suggests using the regression line R=18.00−0.750CR = 18.00 - 0.750CR=18.00−0.750C to estimate the catalyst concentration required to achieve a reaction rate of 5 mol/s. Comment on this suggestion.

[2]
Markscheme

2.5 Data presentation and interpretation Questions

  1. A Level
  2. /Maths
  3. /2.5 Data presentation and interpretation

278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.

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