For 12 employees, x x\,x is length of service in years and y y\,y is the time in hours taken to complete a task. The correlation coefficient between x x\,x and y y\,y is -0.47. For a one-tailed test of negative association at the 5% significance level, the critical value is -0.4973.
Test at the 5% significance level whether there is evidence of negative association. After the transformations m=log10xm=\log_{10}xm=log10x and n=log10yn=\log_{10}yn=log10y, the correlation coefficient is -0.83 and the fitted line is n=0.25−0.16mn=0.25-0.16mn=0.25−0.16m.
Explain why the transformed model is preferable.
Express y y\,y in the form axbax^baxb, giving a a\,a and b b\,b to 3 significant figures where appropriate.
Use the model to predict y y\,y when x=4x=4x=4. Give your answer to 3 significant figures.
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.