Question

Surface roughness of steel is investigated. The method of surface manufacturing largely determines roughness of the surface. One of the parameters to describe the roughness is Rz, the maximum height of the surface irregularities profile. R (in um) is measured for 21 random places on the surface of forged details and 21 random places on the surface of casted details as follows. forge 92 82 86 117 92 105 96 92 109 81 105 96 107 80 105 101 113 110 84 110 83 105 101 97 102 96 103 90 108 92 106 104 108 90 106 107 91 92 89 93 107 96 cast a) Is there evidence to support the claim that the surface of forged steel has a larger surface roughness variance than the surface of casted details? Use a = 0.05. Find the P-value of this test. Round your answer to three decimal places (e.g. 9.876). P-value = i b) Construct a 95% one-sided lower-confidence bound on o 12022. Round your answer to two decimal places (e.g. 9.87). S0120225

Use minitab if possible. If it is, please show step by step process of how you did it.

Answer 1

Descriptive Statistics Select STAT ---> Basic statistics--->2 variances then selct the each sample is in its own column the enter the sample columns Descriptive Statistics Variable N StDev Variance 95% CI for o forge 21 11.780 138.757 (9.012, 17.010) cast 21 6.925 47.962 (5.298, 10.001) Variable forge cast 95% Lower StDev Variance Bound for o 11.780 138.757 9.400 6.925 47.962 5.526 N 21 21 select options, select alternative hypothesis is > select use test & c.l on normal distribution select ok Ratio of Standard Deviations Ratio of Standard Deviations 95% CI for Estimated Ratio using Ratio F 1.70090 (1.083, 2.670) Estimated Ratio 1.70090 95% Lower Bound for Ratio using F 1.167 for confidence intervals in options select alternative hypothesis is # select ok Test Null hypothesis Ho: 01/02 = 1 Alternative hypothesis Hz: 01/02 = 1 Significance level a = 0.05 Test Null hypothesis Ho: 01/02 = 1 Alternative hypothesis Hz: 01/02 > 1 Significance level a = 0.05 here P-value = 0.011 <0.05 so, reject Ho, there is a evidence to support the cliam Method Test Statistic 2.89 DF1 DF2 P-value 20 20 0.022 Method F Test Statistic DF1 2.89 20 DF2 P-value 20 0.011 The 95% confidence interval is (1.083, 2.670)