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).
