You perform a hypothesis test on the claim that the volume in all 12-ounce cans

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 that the mean volume is 12 ounces when it isn't.

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

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

You conclude that the mean volume is 12 ounces when it isn't.

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

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

1

2

1 2

Explanation / Answer

H_0: weight is 12 ounces versus H_1: weight is less than 12 ounces.

(a)Type I error means Reject H_0 when it is true .

    In this context, type I error will be concluding that the mean volume is less than 12 ounce,when it is not true.

(b) Type II error means accepting H_0 when it is not true.

    In this context,type II error will be 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.

(c) Type I error will be alpha, at level of significance alpha

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