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Tensile strength tests were carried out on two different grades of wire rod, resulting in the...

Question:

Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompenying data Sample Mean Size (kg/mm2 SD Sample Sample Grade AISI 1064 126-05.8 -12 AISI 1078126-125.4 2-2.1 a) Does the data provide compelling evidence to cod ding that true a erage strength for the 1078 grade exceeds that or the 1064 grade o more than 10 1 g mm2 Test the appropriate hypotheses uang ล significance level of 0.01. State the relevant mp theses. Calculate the test statistic and μ-value. (Round Your test statistic to two dear7al places and your p-value to four decimal laces. State the conclusion in tha problem context. Fail to reject Ho. The data suggests that the true average strengsh fer the 1078 grade exceeds that for the 1054 grade by more than 10 ka/mm2 Rejeeo. The deta does not suggest that the true everage strength for the 1078 grede exceeds thet for the 1064 grade by more than 10 gmm2 Reject Ho h data suggests that the true average strength for the 1078 grade exoeeds that for the 1064 grade by moe than 10 kg/mem2 Fail to reject Hp The cata does not suggest that the true averaga strength for tha 1078 grade exceeds that for the 1064 grade by more than 1D kg/mm2 b 6stimete the difference between tre dverage strengths or he two gredes in 8 ey that provides n o mation about precs on ard re abity (Use a 95% о nfiderce interval. Round your dre ers to two dear el plates kgym You may reed to use the appropriate table in the Appendix of Tables to answer this question Need Help?

Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompenying data Sample Mean Size (kg/mm2 SD Sample Sample Grade AISI 1064 126-05.8 -12 AISI 1078126-125.4 2-2.1 a) Does the data provide compelling evidence to cod ding that true a erage strength for the 1078 grade exceeds that or the 1064 grade o more than 10 1 g mm2 Test the appropriate hypotheses uang ล significance level of 0.01. State the relevant mp theses. Calculate the test statistic and μ-value. (Round Your test statistic to two dear7al places and your p-value to four decimal laces. State the conclusion in tha problem context. Fail to reject Ho. The data suggests that the true average strengsh fer the 1078 grade exceeds that for the 1054 grade by more than 10 ka/mm2 Rejeeo. The deta does not suggest that the true everage strength for the 1078 grede exceeds thet for the 1064 grade by more than 10 gmm2 Reject Ho h data suggests that the true average strength for the 1078 grade exoeeds that for the 1064 grade by moe than 10 kg/mem2 Fail to reject Hp The cata does not suggest that the true averaga strength for tha 1078 grade exceeds that for the 1064 grade by more than 1D kg/mm2 b 6stimete the difference between tre dverage strengths or he two gredes in 8 ey that provides 'n o mation about precs on ard re abity (Use a 95% о nfiderce interval. Round your dre ers to two dear el plates kgym You may reed to use the appropriate table in the Appendix of Tables to answer this question Need Help?

Answers

here,

test hypothesis:

H0 :  /1 1064ー,11078一一10

Ha : \mu_{1064}-\mu_{1078}>-10

Z - statistic = ((X1-X2) - (-10)) / (sqrt(sigma1^2/n1 + sigma2^2))

= -9.8 / 0.2155

= -45.48

p - value = 0.00001

conclusion ; option - 4

b) for 95% of CI, Z = 1.96

interval = (105.8-125.4) +/- 1.96*0.2155

= -19.8 +/- 0.4224

= (-20.22 , -19.38)

.

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