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
| ttt | 1 | 3 | 6 | 9 | 11 | 15 | 20 |
| www | 92 | 76 | 65 | 50 | 46 | 33 | 25 |
The data is coded using the changes of variable x=tx = tx=t and y=log10wy = \log_{10} wy=log10w
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
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.
Give an interpretation of the constant a a\,a in this equation.
Explain why this model is not reliable for calculating the temperature after 1 hour.
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.