An engineering laboratory is testing the filtration rates of two different synthetic membranes, Graphene-A and Ceramic-B, to determine their efficiency in industrial water treatment. A researcher records the filtration rates (in litres per minute) for 120 samples of Membrane A and 100 samples of Membrane B. The data collected is summarized in the table below:
| Membrane Type | Sample Size (nnn) | Mean Filtration Rate (μμμ) | Sample Variance (s2s^2s2) |
|---|---|---|---|
| Graphene-A | 120 | 48.5 | 18.4 |
| Ceramic-B | 100 | 47.1 | 14.8 |
The researcher claims that there is no significant difference between the mean filtration rates of these two types of membranes.
Test the researcher's claim at the 5% significance level. You should state your hypotheses, test statistic, and critical value clearly.
Explain the significance of the Central Limit Theorem in the context of the test performed in part (a).
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.