Question

9.1.3 GO Tutorial A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho : u = 12 against H :u < 12, using a random sample of 4 specimens. Round your answers to 4 decimal places. (a) What is the type I error probability if the critical region is defined as i < 11.5 kilograms? The type I error probability is (b) Find ß for the case where the true mean elongation is 11.22 kilograms. B=L (C) Find ß for the case where the true mean is 11.5 kilograms. Statistical Tables and Charts

Answer 1

a)

type I error alpha =

P(X<11.5)

=P(z<(11.5-12)*sqrt(4)/0.5)=

P(Z<-2)=

0.0228

b)

beta=

P(X>11.5)

=P(Z>(11.5-11.22)*sqrt(4)/0.5)=

P(Z>1.12)=

1-P(Z<1.12)=

1-0.8686=

0.1314

c)

beta =

P(X>11.5)

=

P(Z>0)=

1-P(Z<0)=

1-0.5=

0.5000