Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. (a) Doe

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Tensile strength tests were carried out on two different grades
of wire rod, resulting in the accompanying data.
(a) Does the data provide compelling evidence for concluding
that true average strength for the 1078 grade exceeds that for the
1064 grade by more than 10 kg/mm2? Test the appropriate
hypotheses using a significance level of 0.01. State the relevant
hypotheses.
H0: 𝜇1064 − 𝜇1078 = −10
Ha: 𝜇1064 − 𝜇1078 ≤ −10H0: 𝜇1064 − 𝜇1078 = −10
Ha: 𝜇1064 − 𝜇1078 ≥ −10 H0: 𝜇1064 − 𝜇1078 = −10
Ha: 𝜇1064 − 𝜇1078 < −10H0: 𝜇1064 − 𝜇1078 = −10
Ha: 𝜇1064 − 𝜇1078 > −10H0: 𝜇1064 − 𝜇1078 = −10
Ha: 𝜇1064 − 𝜇1078 ≠ −10
Calculate the test statistic and 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
true average strength for the 1078 grade exceeds that for the 1064
grade by more than 10
kg/mm2.Reject H0. The data does
not suggest that the true average strength for the 1078 grade
exceeds that for the 1064 grade by more than 10
kg/mm2. Fail to
reject H0. The data does not suggest that
the true average strength for the 1078 grade exceeds that for the
1064 grade by more than 10 kg/mm2.Fail to
reject H0. The data suggests that the true
average strength for the 1078 grade exceeds that for the 1064 grade
by more than 10 kg/mm2.
(b) Estimate the difference between true average strengths for the
two grades in a way that provides information about precision and
reliability. (Use a 95% confidence interval. Round your answers to
two decimal places.)
,
kg/mm2