A marine biologist monitored the concentration of microplastics in a bay. She took 80 water samples from random locations and found the mean concentration to be 54 mg/L54 \text{ mg/L}54 mg/L with a standard deviation of 15 mg/L15 \text{ mg/L}15 mg/L. After a new filtration system was installed at a nearby treatment plant, she took 120 more samples and found the mean concentration to be 49 mg/L49 \text{ mg/L}49 mg/L with a standard deviation of 8 mg/L8 \text{ mg/L}8 mg/L.
Test at the 1%1\%1% level of significance whether the mean concentration of microplastics in the bay decreased after the filtration system was installed. State your hypotheses clearly.
Explain the significance of the Central Limit Theorem to the test in part (a).
State an assumption you have made about the sample variances to carry out this test.
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.