Question

5. A firm has just developed a new cost-reducing technology for producing a certain replacement part for tractors. Since a replacement part must be produced within close specifications in order for it to be acceptable for customers, the new technology's specifications must not deviate much from the older version. Suppose the sample standard deviation for 15 parts randomly sampled from the older version is .53. A random sample of 14 parts produced using the new technology results in a sample standard deviation of .75. At the .05 level of significance, test to see if the variances are different. List and clearly label all eight steps.

Answer 1

we have to test that if two standard deviations are equal so

$H_0: \sigma_1=\sigma_2,H_a: \sigma_1 \neq \sigma_2$

older parts have

S1=0.53 n1=15

new parts

S2=0.75 n2=14

for testing we will use F statistics

$F=\frac{S_2^2}{S_1^2}=\frac{0.75^2}{0.53^2}=2.002$

F will have DF =[(n2-1),(n1-1)]=[(14-1),(15-1)]=(13,14)

since test is two tailed so P Value is given by

P-Value =2*P(F13,14>2.004) =2*0.105=0.210

Since P Value is higher than level of significance hence we do not reject H0 hence there is no sufficient statistical evidence to conlcude that two standard deviations are unequal.