The production supervisor of an assembly line for producing cheeses suspects that the weight of the...

The production supervisor of an assembly line for producing cheeses suspects that the weight of the bags produced is higher than the specification of 200 g. She would like to take a simple random sample of bags of cheeses produced by the assembly line and perform a statistic test to confirm that this is indeed the case. (6 points)

What would be the null and alternative hypothesis for this research?
What is the type I error in general and in this situation?
What is the type II error in general and in this situation?

Solutions

Expert Solution

Solution

Part a)

Our Hypotheses

Null hypothesis : weight >200 gm

Against

Alternate Hypothesis : weight ≤ 200 gm

Part b)

Type 1 Error

In General - Rejecting the null hypothesis Ho when Ho is True.

It is also called Producer's Risk.

In this Situation - Rejecting the claim that weight is greater than 200 gm though it is actually greater than 200 gm.

Rejection of null means the specification that will be less than or equal to 200g is acceptable

Part c)

Type 2 Error

In General - Accepting the null hypothesis Ho when Ho is False.

It is also called Consumer's Risk.

In this Situation - Acceptingthe cclaim that weight is greater than 200 gm though it is not greater than 200 gm or Ho is False and we're accepting it.

It will mean that we are accepting the wrong hypothesis which will lead to loss of customer while buying that product.

Please see the attached file.

orchestra answered 1 year ago

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