18 Fair Packaging and Labeling Federal law requires that a j

18. Fair Packaging and Labeling Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least 32 ounces. A consumer advocate feels that a certain peanut butter manufacturer is shorting customers by under filling the jars.

a) determine the null and alternative hypotheses

(b) explain what it would mean to make a Type I error

(c) explain what it would mean to make a Type II error.

Solution

a) H0: mu >=32

    Ha: mu < 32

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b) type I error is the incorrect rejection of a true null hypothesis (a \"false positive\"),

Here it is incorrect rejection of jar contains atleast 32 oz when it is really true.

c) a type II error is the failure to reject a false null hypothesis (a \"false negative\").

Here it is wrongly accepting jar contains atleast 32 oz when it is actually not.