Question

Tenslle strength tests were carried out on two different grades of wire rod, resulting In the accompanylng data. Sample Mcan Sample Sample (kg/mm2)SU Grade AISI 1064 AISI 1078 Size m-127 n127 s1 _ 1.2 125.3 22.0 x-109.5 (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 o 0.01. State the relevant hypatheses Ho: #1064-#1078-_10 μ1064-11078 -10 Ho: H1064 H107810 ai μ1064-μ1078 2-10 Hai μ1064-#1078 <-10 Calculale lhest stlistic ard Pve. Round ursltic too decimal places and your P-valuelo our demal plaes) z=-76 34 value- State the conclusion in the problem context Reject Hg he data does not suggest that the true average strength for the 10/8 grade exceeds that for the 1064 grade by more tha 10 kg/mm2 ⓔ Reject Ho. The data suggests that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm2 Fail to reject Ho. The data does not suggest that the true average strength for the 1078 grade exceeds that for the 1064 grade hy more than 1a kg/mm2 Fail to reject Ho 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 or the two grades in a way that provides in ormation about precision and reliability use a 95% confidence interval Round your answers to two decimal places. kg/mm2

Having problem solving the z value, my answer that i got was -76.34 and was wrong, also need a better understanding of b

Answer 1

Date: 15/05/2019 Answer a) The z-test statistics is By using Excel, find z-test statistics with the help of following steps is: 1) Import the data. 2) Select the MegaStat from Add-Ins option. 3) Select the Compare Two Independent Groups from Hypothesis Tests 4) Select data input. 5) Select Confidence level, Test difference and alternative hypothesis. 6) Select -test. 7) Click Ok.

Hypothesis Test: Independent Groups (z-test) AISI 1064 AISI 1078 109.5 125.3 mean 1.2 127 2std. dev. 127 n 15.8000 difference (AISI 1064 - AISI 1078) 0.2070 standard error of difference -10 hypothesized difference -28.02 z 0.00E+00 p-value (one-tailed, lower) -162056 confidence interval 95.96 lower -15.3944 confidence interval 95% upper 0.4056 margin of error From the Excel output, the z-test statistics is - 28.02 b) A 95% confidence interval for the difference between true average strengths for the two grades is

From Excel output in part (a), a 95% confidence interval for the difference between true average strengths for the two grades is -16.21 to -15.39