Question

You perform a hypothesis test on the claim that the volume in all 12-ounce cans of Fizzy Pop is less than 12 ounces. In terms of the possible conclusions of this hypothesis test, choose the appropriate description of a Type I and Type II error.

(a) If you make a Type I error, then which of the following is true?

You conclude the mean volume in all cans is less than 12 ounces when that is not true.You conclude that the mean volume is 12 ounces when it isn't.     You don't conclude the mean volume in all cans is less than 12 ounces when in fact, the mean volume is less than 12 ounces.

(b) A Type II error occurs when which of the following is true?

You don't conclude the mean volume in all cans is less than 12 ounces when in fact, the mean volume is less than 12 ounces.You conclude the mean volume in all cans is less than 12 ounces when that is not true.     You conclude that the mean volume is 12 ounces when it isn't.

(c) What is the probability of a Type I error if the significance level is α?

1 − α1 − 2α    2αα

Answer 1

a) Type I error is associated with probability of rejecting the true null hypothesis. So in this case, it will be:

You conclude the mean volume in all cans is less than 12 ounces when that is not true.

Option A is correct.

b) Type II error is associated with the probability of not rejecting the false null hypothesis. So in this case, it will be:

You don't conclude the mean volume in all cans is less than 12 ounces when in fact, the mean volume is less than 12 ounces.

Option A is correct.

c) Probability of Type I error = Significance level = α