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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 181

An industrial ceramicist measures the energy consumption, EEE kWh, required to maintain different operating temperatures, TTT ∘C^{\circ}\text{C}∘C, in a specialized kiln. Data from 6 test runs are recorded in the table below.

Run123456
TTT200250300350400450
EEE4558688295102
∑T=1950,∑E=450,∑T2=677500,∑E2=36166,∑TE=156500 \sum T = 1950, \sum E = 450, \sum T^2 = 677500, \sum E^2 = 36166, \sum TE = 156500 ∑T=1950,∑E=450,∑T2=677500,∑E2=36166,∑TE=156500
a.

Calculate the values of STTS_{TT}STT​, SEES_{EE}SEE​ and STES_{TE}STE​ for these measurements.

[3]
b.

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

[2]
c.

Interpret your result from part (b) in the context of the kiln's operation.

[2]
d.

On a suitable grid, draw a scatter diagram of energy consumption against operating temperature for these 6 runs.

[2]
e.

Determine the equation of the regression line of EEE on TTT in the form E=a+bTE = a + bTE=a+bT.

[3]
f.

Use your regression line to estimate the energy consumption for a run with an operating temperature of 320 ∘C^{\circ}\text{C}∘C.

[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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