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Question 194

The ambient temperature, T ∘CT\,^\circ\text{C}T∘C, and the cooling time, CCC minutes, required for a specialized industrial freezer to freeze a specific chemical sample were recorded on 6 different operating days. The data is summarized in the table below.

Day123456
TTT202225283031
CCC141621263235
∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930 \sum T = 156, \quad \sum C = 144, \quad \sum T^2 = 4154, \quad \sum C^2 = 3818, \quad \sum TC = 3930 ∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930
a.

Calculate the values of SCCS_{CC}SCC​, STCS_{TC}STC​ and STTS_{TT}STT​ for these data.

[3]
b.

Calculate the product moment correlation coefficient (PMCC) for these data.

[2]
c.

Interpret your value of the PMCC in the context of the relationship between ambient temperature and cooling time.

[1]
d.

On a suitable grid, draw a scatter diagram of cooling time against ambient temperature for these 6 days.

[3]
e.

Determine the equation of the regression line of CCC on TTT in the form C=a+bTC = a + bTC=a+bT.

[3]
f.

Use your regression line to estimate the cooling time required when the ambient temperature is 27 ∘C27\,^\circ\text{C}27∘C.

[2]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
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