Many older homes have electrical systems that use fuses rather than circuit brea

Question

Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40. If the mean amperage is lower than 40, customers will complain because the fuses require replacement too often. If the mean amperage is higher than 40, the manufacturer might be liable for damage to an electrical system due to fuse malfunction. To verify the amperage of the fuses, a sample of fuses is to be selected and inspected. If a hypothesis test were to be performed on the resulting data, what null and alternative hypotheses would be of interest to the manufacturer? State the null hypothesis. State the alternative hypothesis. Ha: ? 40 Describe the type I error in the context of this problem situation. declaring a fuse as being defective when in fact there is nothing wrong with it choosing the wrong type of significance test declaring a fuse as being satisfactory when in fact it is not testing the wrong hypotheses Describe the type II error in the context of this problem situation. declaring a fuse as being satisfactory when in fact it is not choosing the wrong type of significance test testing the wrong hypotheses declaring a fuse as being defective when in fact there is nothing wrong with it

Explanation / Answer

Answer to the question is as follows:

Since, its a matter of tasting for equality, therefore we have equality in null hypothesis.

Ho: Mu = 40
Ha: Mu!=40

A type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).

The type 1 error situation is :
Option 1 is right. Declaring a fuse as being defective when in fact there is nothing wrong with it.

The type 2 error in the context of this problem is :
Option 1 is right. Declaring a fuse as being satisfactory when in fact it is not.

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