Question

Management of El Burrito decides that if their burritos are larger than the standard weight of 1.2 lb, drink sizes will have to be reduced to compensate for the loss of profits. For a one-sided hypothesis test where H0: = 1.2 lb, Ha: > 1.2 lb, and = .01, which of these statements represents a Type I error in this scenario, and what's the probability of making such an error?

A. The average burrito is less than 1.2 lb, and the company increases drink size. P(Type I error) = .99.

B. The average burrito is greater than 1.2 lb, but the company doesn't change drink sizes. P(Type I error) = .99.

C. The average burrito is actually 1.2 lb, but the test concludes that the burrito is larger than 1.2 lb. The company decreases drink sizes. P(Type I error) = .01.

D. The average burrito is actually 1.2 lb, but the test concludes that the burrito is larger than 1.2 lb. The company decreases drink sizes. P(Type I error) = .99.

E. The average burrito actually weighs more than 1.2 lb, but the test incorrectly concludes that average burrito weight is 1.2 lb. Drink sizes aren't changed. P(Type I error) = .01.

Answer 1

We know that the definition of Type 1 error is ,

P(Type I Error)= Probability of rejecting a true null hypothesis.

As per the question, the Null hypothesis is that the average size of the burrito is 1.2 lb and the alternative hypothesis is that the average size of the burrito is greater than 1.2 lb and that the probability that the null hypothesis is rejected is given as 0.01(Size of the test).

According to the statement of the Type I Error, the Null hypothesis is true i.e. the actual size of the burrito IS 1.2 lb. Also, the test concludes that the alternate hypothesis is true i.e. the size of the burrito is larger than 1.2 lb. Moreover, since the probability of rejection of Null hypothesis is given as 0.01, by definition the of type 1 Error, P(Type 1 Error)=0.01.

So, the correct option is :

C. The average burrito is actually 1.2 lb, but the test concludes that the burrito is larger than 1.2 lb. The company decreases drink sizes. P(Type I Error)= .01.