Answer to Question #208625 in Statistics and Probability for Humphrey

Question

A manager at a supermarket claims that the average weight of loaves of bread they sell is 400g. An official from the Consumer Protection Commission takes a random sample of 50 loaves of bread and decides he will reject the claim if the sample menu is less than 390g. The sample standard deviation of the 50 loaves is found to be 25g.

a) Explain how type II error would be committed in this context.

b) Find the probability of committing a type I error.

c) Find the probability of committing a type II error if the true mean weight is 381g.

Answer 1

$\mu=400, x=390,n=50,s=25$

Let Null hypothesis-

$H_o:\bar{x}\ge 390$ g , claim is true

And $H_a:\bar{x}<390g,$ Reject the claim.

(a) Type II error is will be committed When we claim is not rejected and The true value of the weight is less than 390g.

(b) Probability of computing type I error-

P(type I error)=$P(z>\dfrac{390-400}{25})=P(z>-0.4)=$ 0.655

(c)probability of committing a type II error if the true mean weight is 381g.

$P(z<\dfrac{381-400}{25})=P(z<-0.76)=0223$