Question

2.2 In an experiment involving the breaking strength of a filament, one batch of filament was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strength (in N) of the filament was measured. Find a 95% confidence interval for the mean difference between the mean breaking strengths. Do your results support the idea that the breaking strengths are the same? Treatment Sample Size (n) Average StDev N N 7 48.86 5.70 8 59.88 4.42 60 Seconds 120 Seconds

Answer 1

From sample For 60 seconds 120 seconds 12 = 8 X2 = 59.88 S2 = 4.42 ni 7 Xi 48.86 S = 5.7 Here population variances are not equal is t distribution sir 32 df for df a 2 ru S2 3, ni f ㅗ 1₂-1 ne n, 1 2 5.7 4.42 + 8 7 2 114.42 7 8 6 ~ 11 2 df = 17.29 Standard Exsor (SE) 3, 4.42 5.7 7 + + nz 8 2.6615 t*t score for 95%. confidence with df = 11 € 2.201 : 95% contidence interval for Mean difference -((51-x))+ t.se), - [(18.86 – 59-88) + 2. 201x 2.6615 ( - 11.02 + 5.86) (-16.88, -5:16) - TI

Clearly the confidence interval doesn't contains the point 0 . Which indicates that there is no evidence that the mean difference is 0 .

So the results doesn't support that the breaking strengths are the same .