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2.5.5 Hypothesis test for the mean of a normal distribution (A-level only)

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Question 23

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:

MaterialSample size (nnn)Sample mean (xˉ\bar{x}xˉ)Sample variance (s2s^2s2)
Alloy A55412.585.4
Alloy B68384.262.1
a.

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.

[8]
b.

State two assumptions you have made in carrying out the test in part (a).

[2]

2.5.5 Hypothesis test for the mean of a normal distribution (A-level only) Questions

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