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).
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.