Management of El Burrito decides that if the 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 II error for this scenario?

A. The test concludes that the average burrito is 1.2 lb and the company increases drink sizes.

B. The test concludes that the average burrito is greater than 1.2 lb, but the actual average is 1.2 lb. Drink sizes are reduced.

C. Drink sizes are kept the same because the null hypothesis is not rejected, but the actual weight of burritos is greater than 1.2 lb.

D. The average burrito weighs 1.2 lb, the null hypothesis is not rejected, and drink sizes are kept the same.

E. The test reveals that the average burrito weighs less than 1.2 lb and drink sizes are increased.

A type II error is defined "as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population"

Solution to the problem

The system of hypothesis are on this case:

H0: [tex]\mu =1.2[/tex]

So then the alternative hypothesis, by the complement rule is:

Ha: [tex]\mu >1.2[/tex]

Based on this we can conclude that the correct options on this case would be:

C. Drink sizes are kept the same because the null hypothesis is not rejected, but the actual weight of burritos is greater than 1.2 lb.

Is the mist complete option and the reason why is because we are retaining or FAIL to reject the null hypothesis when actually is FALSE.