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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 75

The temperature of water (w∘Cw^\circ\text{C}w∘C) in a kettle t t\,t minutes after it was boiled is recorded in the table below

ttt1369111520
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The data is coded using the changes of variable x=tx = tx=t and y=log⁡10wy = \log_{10} wy=log10​w

The regression line of x x\,x on y y\,y is found to be y=1.99−0.031xy = 1.99 - 0.031xy=1.99−0.031x

a.

Given that the data can be modelled by an equation in the form w=abtw = ab^tw=abt where a a\,a and b b\,b are constants. Find the values of a a\,a and b b\,b to 3 significant figures.

[3]
b.

Give an interpretation of the constant a a\,a in this equation.

[1]
c.

Explain why this model is not reliable for calculating the temperature after 1 hour.

[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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