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).
Practise Edexcel A Level Maths Hypothesis Testing with the Normal Distribution with exam-style questions for A Level Maths. 132 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
