An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For m = 33 specimens, the sample average toughness was x = 63.1 for the high-purity steel, whereas for n = 36 specimens of commercial steel y = 57.6. Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both toughness distributions are normal.
(a) Assuming that σ1 = 1.4 and
σ2 = 1.1, test the relevant hypotheses using
α = 0.001. (Use μ1 −
μ2, where μ1 is the average
toughness for high-purity steel and μ2 is the
average toughness for commercial steel.)
State the relevant hypotheses.
H0: μ1 −
μ2 = 5
Ha: μ1 −
μ2 ≤ 5 H0:
μ1 − μ2 = 5
Ha: μ1 −
μ2 < 5
H0: μ1 −
μ2 = 5
Ha: μ1 −
μ2 ≠ 5 H0:
μ1 − μ2 = 5
Ha: μ1 −
μ2 > 5
Calculate the test statistic and determine the P-value.
(Round your test statistic to two decimal places and your
P-value to four decimal places.)
z | = | |
P-value | = |
State the conclusion in the problem context.
Reject H0. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. Fail to reject H0. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. Reject H0. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
Fail to reject H0. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
(b) Compute β for the test conducted in part (a) when
μ1 − μ2 = 6. (Round your
answer to four decimal places.)
β =
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