Question

Use the measured TBN values of fresh Rotella T6 synthetic and Xtreme Synthetic Blend oils in the Oil dataset. Use Excel to:

a. Construct the 95 percent CI for the standard deviation of TBN for each oil type.

b.Test at the 5 percent significance level whether the variance in the T6 oil is less than that in the blend oil.

Shell Rotella T6 Synthetic Oil New Oil Xtreme Synthetic Blend New Oil Sample Viscosity (cSt)TBN (mg KOH/g) Sample 13.07 12.45 12.52 14.29 12.36 13.74 12.83 13.15 12.60 12.58 13.09 12.81 12.68 12.60 13.97 12.76 12.81 12.17 12.28 12.52 14.35 13.58 12.07 12.84 12.77 12.55 12.33 12.63 12.50 12.36 12.65 12.67 13.53 12.81 12.82 13.39 TBN (mg KOH/g) 8.20 8.26 8.06 8.66 8.56 8.56 8.26 8.16 8.06 8.16 8.06 8.16 9.00 8.96 9.06 8.96 9.06 9.06 8.86 8.86 8.86 8.96 9.06 8.86 10.30 9.62 9.62 10.60 9.86 9.72 9.62 9.52 10 9.42 10.06 9.56 9.52 9.42 10.06 9.62 9.52 9.52 9.52 9.42 10.10 9.56 9.42 9.86 9.62 10 12 12 15 16 15 16 18 19 20 21 18 19 23 23 26 27 9.52 9.42 9.42 9.42 9.42 9.52 9.42 9.52 9.42 9.42 29 30 35

Answer 1

CI (0226,0.363) For Blend Oil: MINITAB Procedure Step 1: Choose Stat > Basic Statistics > 1 Variance Step 2: Under Data, choose Sample in column Step 3: Enter Synthetic Oil Step 4: Select Options and enter the Confidence level as 95.0 and Alternative as not equal. Click OK. Step 5: Click OK. MINITAB output: Test and Ci for One Variance: Blend Oil Method The chi-square method is only forehe normal distribusion. The Bonett nethod is for any continuous distribution Statistics Variable Blend oil 24 0.391 N StDev Variance 0-153 95% Confidence Interval# CI tor Variance Variable Hethod ci for stDev Blend 0i1 Chi-square (0.304, О.S48) (0.092, 0.301) (0.346, 0.481 (0.120, 0.232) Bonett

From the MINITAB output, the 95% confidence interval for Standard deviation is, CI-(0304,0.548) Conduct the test. Null hypothesis: Alternative hypothesis: MINITAB procedure: Step 1: Choose Stat > Basic Statistics > 2 Variance Step 2: Under Data, choose Sample in different columns. Step 3: In First, enter Synthetic Oil. Sterp 4: In Second, enter 341 under Sample size. Step 5: In Second, enter Blend Oil Step 6: Check Options, enter Confidence level as 95.0. Step 7: In Hypothesized ratio Variance 1 Variance 2 Step 8: Choose less than in alternative. Step 9: Click OK in all dialog boxes. MINITAB output:

Test and Ci for Two Variances: Synthetic O, Blend O Alternative ๒rpothesi฿ variance(synthesie ฮเ1) / variance(Blend 011, < 1 siqnificance Level Aipha-0.05 synthetie 041 36 0.27 Bland d 0.359 0,353 o of variances o 0-50 Opper bound pper und Distribusios or s ontinuous ง.58 0.002 From the MINITAB output, the p-value is, p-value 0.034 Sincea p-value < 0.05, thus, the null hypothesis is rejected at 5% level of significance Therefore, it can be concluded that the variance oil Synthetic Oil is less than that of Blend Oil.