A materials scientist asserts that the mean tensile strength of high-performance Alloy A exceeds the mean tensile strength of standard Alloy B by more than 25 MPa.
A random sample of 55 specimens of Alloy A and 68 specimens of Alloy B is tested. The tensile strength, sss, in MPa, is recorded for each specimen. The results are summarized in the following table:
| Material | Sample size (nnn) | Sample mean (xˉ\bar{x}xˉ) | Sample variance (s2s^2s2) |
|---|---|---|---|
| Alloy A | 55 | 412.5 | 85.4 |
| Alloy B | 68 | 384.2 | 62.1 |
Conduct a hypothesis test at the 5% level of significance to investigate the scientist's assertion. State clearly your hypotheses, the value of your test statistic, and the critical value.
State two assumptions you have made in carrying out the test 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.