An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity

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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 = 64.3 for the high-purity
steel, whereas for n = 36 specimens of
commercial steel y = 58.6. 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 = 1.3 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 >
5H0: 𝜇1 − 𝜇2 =
5
Ha: 𝜇1 − 𝜇2 <
5 H0: 𝜇1 − 𝜇2 =
5
Ha: 𝜇1 − 𝜇2 ≠ 5H0: 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.)
State the conclusion in the problem context.
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. 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 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 =