An engineering laboratory is conducting research on the tensile strength of two newly developed carbon-fiber composites, Apex and Zenith. A quality control engineer randomly selects 250 samples of composite Apex and 250 samples of composite Zenith. The tensile strength measurements (in MPa) are summarized in the following table:
| Composite | Mean Tensile Strength (xˉ\bar{x}xˉ) | Variance of Strength (s2s^2s2) |
|---|---|---|
| Apex | 455.5 | 1800 |
| Zenith | 447.1 | 2200 |
The engineer asserts that there is no significant difference between the mean tensile strengths of these two composites.
Evaluate the engineer's assertion at the 5% significance level. You must clearly state your hypotheses, the calculated test statistic, and the critical value(s) used.
Discuss the importance of the Central Limit Theorem in the context of the test performed in part (a).
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.