Question

In: Statistics and Probability

A Fritos bag is supposed to contain 9. 25 oz of chips. In the packaging plant,...

A Fritos bag is supposed to contain 9. 25 oz of chips. In the packaging plant, a sample of bags is taken every few days to make sure the machine is dispensing the correct amount of Firtos. Thus, the quality control specialist is testing the hypotheses:

Ho: μ=9.25

Ha: μ ≠ 9.25

A) Describe what a Type I error would be in terms of the problem?

B) Describe what a Type II error would be in terms of the problem?

C) What are the consequences of making a type I error? What action would be taken?

D) What are the consequences of making a type II error? What action would be taken?

E) In your opinion, which error is worse to make? Explain why.

Solutions

Expert Solution

Ho: μ=9.25 (Fritos bag contains 9.25 oz of chips on avg.)

Ha: μ ≠ 9.25 (Fritos bag does not contain 9.25 oz of chips on avg.)

Type 1 error: To reject a true null hypothesis.

Type 2 error: To accept a false null hypothesis.

A) Describe what a Type I error would be in terms of the problem?

Reject null hypothesis: Fritos bag does not contain 9.25 oz of chips on avg.

True null hypothesis: avg. chips = 9.25 oz.

Type 1: Rejecting the claim that Fritos bag does contain on avg. 9.25 oz of chips when in fact it is 9.25 oz.

B) Describe what a Type II error would be in terms of the problem?

Accept null hypothesis: Fritos bag contains 9.25 oz of chips on avg.

False null hypothesis: avg. chips not equals 9.25 oz

Type 2:Accepting the claim Fritos bag contains on avg. 9.25 oz of chips when in fact it is not  9.25 oz.

C) What are the consequences of making a type I error? What action would be taken?

The chance of rejecting the null hypothesis reduces by taking lower level of significance. But if the null hypothesis is false, then lower significance that is making type 1 error will reduce but probabililty of type 2 error will increase.Here the consequence is the we concldue that the Fritos bag does not contain 9.25 oz when in fact it does. therefore to reduce the type 1 error level of significance can be reduced.

D) What are the consequences of making a type II error? What action would be taken?

The chance of accepting the null hypothesis will be reduced by taking higher values of level of significance. But if the null hypothesis is true, then higher level of significance will increase the probability of making type 1 error. Here the consequence is the we concldue that the Fritos bag does contain 9.25 oz when in fact it does not. therefore to reduce the type 2 error level of significance can be increased.

E) In your opinion, which error is worse to make? Explain why.

Type 1 error of conluding to reject the true null hpothesis is worse because that means the is supposed to contain 9.25 and it is containing that much. But because we rejected this claim we will need to make changes to bring to the level of 9.25 without any reason to.


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