An environmental researcher believes that there is a positive correlation between the average daily temperature in a city and the concentration of ground-level ozone.
The researcher collected data from a random sample of 40 days.
The product moment correlation coefficient (PMCC) between the temperature and ozone concentration for this sample was 0.38.
Carry out a hypothesis test at the 1% significance level to determine if this sample provides sufficient evidence to support the researcher's belief.
For n=40n = 40n=40, the critical value for a one-tailed test at the 1% level for the population correlation coefficient is 0.3665.
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.