A glaciologist suggests that there is a negative correlation between the concentration of a specific microplastic, ppp parts per billion, in snow samples and the distance, ddd km, from the nearest research station.
The glaciologist analyzed a random sample of 25 locations and calculated the product moment correlation coefficient (PMCC) between the microplastic concentration and distance to be −0.415-0.415−0.415.
Carry out a hypothesis test at the 5% significance level to determine if this sample provides sufficient evidence to support the glaciologist's suggestion.
For n=25n = 25n=25, the critical value for a one-tailed test at the 5% level for the population correlation coefficient is 0.33650.33650.3365.
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.