The temperature of water in a kettle is www °C at time t t\,t minutes after boiling. A regression model fitted over the first 20 minutes is log10w=1.99−0.031t\log_{10}w=1.99-0.031tlog10w=1.99−0.031t.
Express the model in the form w=abtw=ab^tw=abt, giving a a\,a and b b\,b to 3 significant figures.
Interpret a a\,a in context.
Explain why the model is unlikely to be reliable after 60 minutes.
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.