The label on a 3-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.
(a) Develop the appropriate null and alternative hypotheses.
(b) What is the Type I error in this situation?
(c) What is the Type II error in this situation?

Respuesta :

Answer:

a.) The Null Hypothesis can be said to be: [tex]H_{0} : \mu \leq 1 gram[/tex]

   The Alternate Hypothesis can be: [tex]H_{a} : \mu > 1 gram[/tex]

For b.) and c.) please see explanation below

Step-by-step explanation:

a.) The Null Hypothesis can be said to be that the 3 quart container contains less than or equal to 1 gram of fat

[tex]H_{0} : \mu \leq 1 gram[/tex]

Therefore the Alternate Hypothesis can be that the 3 quart container contains more than 1 gram of fat

[tex]H_{a} : \mu > 1 gram[/tex]

b.) In Type I Errors  the given Null hypothesis is rejected when in fact it is true.

In this situation the Type I error would be that the statement that the 3 quart container contains less than or equal to 1 gram of fat is rejected when it is actually true.

c.) Type II errors are those where the Null Hypothesis is false but is not rejected.

In this situation the Type II error would be that the statement that the 3 quart container contains less than or equal to 1 gram of fat is false but it is not rejected.