Question

Stats problem, will rate and comment
In order to inspect the fat content of hamburger meat used in her restaurant, an owner randomly samples the meat and the fat percentage is calculated for the sample. The owner needs the fat content to be less than 20%. If the fat content is 20% or more, then she will return the meat to her supplier which will cause a shortage of meat for that day. Her hypotheses are as follows:

H₀: p = 0.20

H_A: p < 0.20

a. What is a Type I error in the context of this problem, and what are its consequences?

b. What is a Type II error in the context of this problem, and what are its consequences?

Q) If I do not reject the null when alpha = 0.03, would I make the same decision if alpha = 0.02? Explain.

Answer 1

a) type 1 error is rejecting a true null hypothesis .

That means we reject p = 0.20 , and accept all the meat whose fat contents are not less than 20%

b) type 2 error is accepting a false null hypothesis

that means we accept p = 0.20 , and send back the meat which had fat contents less than 20% , thereby creating a shortage

For alpha = 0.03 , critical value of z is 1.89

for alpha = 0.02 , critical value of z is 2.06

so if we don’t reject at alpha = 0.03

that means test statistic is less than 1.89

so we reject the null hypothesis at alpha = 0.02 too