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, $s$ , in MPa, is recorded for each specimen. The results are summarized in the following table:

Material	Sample size ( $n$ )	Sample mean ( $xˉ\bar{x}$ )	Sample variance ( $s^2$ )
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).

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, $s$ , in MPa, is recorded for each specimen. The results are summarized in the following table:

Material	Sample size ( $n$ )	Sample mean ( $xˉ\bar{x}$ )	Sample variance ( $s^2$ )
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).

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 22

Markscheme

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 22

Markscheme

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 22

2.5.3 Hypothesis test for a Normal mean (A-level only) Questions

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 22

2.5.3 Hypothesis test for a Normal mean (A-level only) Questions