Stuck with type two error

SadieKhan

TS Contributor
#1
2. A production process makes steel bars used for bridge support has an average weight μ of 36.0 lb. The standard deviation is 4.0 lb. The size of the sample taken is 64 bars. It is important that the bars not be too light or too heavy. Assuming that α= 0.01 for a two sided confidence limits and that we wish to set critical values for the acceptance or rejection of the production runs. The Lower and Upper critical limits or the dividing line of criteria are respectively C1 and C2.
If the true mean μ1=38.25 lb., compute the probability of a type II error (β) assuming that the type I error has not changed. Sketch and indicate the probability (or the region) of the type II error.
Solution

critical values are
C1= 34.71
C2 = 37.29
Type II error = p (fail to reject H0, when H1 is true)
=P(34.71 <Xbar< 37.29 | μ1=38.25)
=p(34.71- 38.25/0.5<xbar- /σ/sqrt(n)< 37.29- 38.25/0.5|1= 38.25)
= P(-7.08<z<-1.92)
= 0.0274

something is wrong, dont know what.:(
Thanks
 
#2
f the true mean μ1=38.25 lb., compute the probability of a type II error (β) assuming that the type I error has not changed.
What do you mean by true mean? I guess you have already specified true population mean as 36.0 lbs in first line. In your calculation, you have used this value as alternative hypothesis. (u1 = 38.25)
=p(34.71- 38.25/0.5<xbar- /σ/sqrt(n)< 37.29- 38.25/0.5|1= 38.25)
I think value in the denominator should be 2.