can I get help with A B and C Statistics A manufacturer pr

can I get help with A) B) and C) ?

Statistics . A manufacturer produces its products with two different procedures that, on 379 average, both approximately products the same number of products per day A consultant for the manufacturer recommends that out of the two procedures, the one with the smaller variance in the output product per day stays permanently To test the recommendation of the consultant, t one from product of each procedure were taken and the following data were observed: edures that, on the two independent random samples Procedure 2 Procedure 1 /21 21 days 1432 S 1 21 days 3761 variances in the number of units produced per day differ for the tu nrnçedures? (a) Do these data provide sufficient evidence at -0.10 to conclude that th nnt (a) is affimative, which procedure should

Solution

There are given two procedures procedure1 and procedure2.

n1 = 21

s1² = 1432

n2 = 21

s2² = 3761

Here we have to test the hypothesis that the variances in the number of units produced per day differ for the two procedures.

that is

H0 : 1² = 2²  Vs H1 : 1² 2²

alpha = 0.10

The test statistic for testing is,

F = larger variance / smaller variance = s2² / s1²

F = 3761 / 1432 = 2.6264

d.f for numerator = n2 - 1 = 21 - 1 = 20

d.f. for denominator = n1 - 1 = 21 - 1 = 20

Critical value we can find by using EXCEL.

syntax :

=FINV ( probability,deg_freedom1 , deg_freedom2)

probability = alpha /2

deg_freedom1 = 20 ,

deg_freedom2 = 20

critical value = 2.1242

F > critical value

reject H0 at 10% level of significance.

Conclusion : The two variances are not equal.