Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Grade Sample Sample Sample
Size Mean SD
(kg/mm2)
AISI 1064 m = 126 x = 102.8 s1 = 1.2
AISI 1078 n = 126 y = 121.3 s2 = 2.0
(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 the P-value approach. (Use H0: μ1064 − μ1078 = −10 versus Ha: μ1064 − μ1078 < −10. 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.
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.
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.
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.Your answer is correct.
(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