Question

In: Statistics and Probability

The label on a 4-quart container of orange juice states that the orange juice contains an...

The label on a 4-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.

a) H₀: μ = 1

b) H_a: μ ≠ 1

a) H₀: μ > 1

b) H_a: μ ≤ 1

a)H₀: μ ≥ 1

b) H_a: μ < 1

a) H₀: μ < 1

b) H_a: μ ≥ 1

a) H₀: μ ≤ 1

b) H_a: μ > 1

(b)What is the type I error in this situation? What are the consequences of making this error?

a) It is claiming μ < 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.

b) It is claiming μ > 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.

c) It is claiming μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

d) It is claiming μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

(c) What is the type II error in this situation? What are the consequences of making this error?

a) It is concluding μ > 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.

b) It is concluding μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

c) It is concluding μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

d) It is concluding μ < 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.

Expert Solution

a) Here we have the label on a 4-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. we have to test the claim on the label. The claim on the label is an average of 1 gram of fat or less. Hence the answer is

b) type 1 error is rejecting the null hypothesis when it is true. The claim on the label is an average of 1 gram of fat or less. hence the answer is

It is claiming μ > 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.

c) type 2 error is, do not reject(accept) the null hypothesis when the alternative hypothesis is true. that is the claim on the label is an average of 1 gram of fat or less is actually false but we accept it. hence the answer is

It is concluding μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

orchestra answered 1 year ago

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