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?

H0: > 40

Ha: = 40

H0: = 40

Ha: 40

    

H0: = 40

Ha: < 40

H0: = 40

Ha: > 40

H0: < 40

Ha: = 40

Describe type I error in the context of this problem situation.

A type I error would be declaring a fuse to be satisfactory when in fact it is defective.

A type I error would be declaring a fuse to be satisfactory when in fact it is satisfactory.    

A type I error would be declaring a fuse as being defective when in fact there is nothing wrong with the fuse.

A type I error would be declaring a fuse as being defective when in fact the fuse is defective.

Describe type II error in the context of this problem situation.

A type II error would be declaring a fuse to be satisfactory when in fact it is defective.

A type II error would be declaring a fuse to be satisfactory when in fact it is satisfactory.    

A type II error would be declaring a fuse as being defective when in fact there is nothing wrong with the fuse.

A type II error would be declaring a fuse as being defective when in fact the fuse is defective.

Many older homes have clectrical systcms that usc fuscs rather than circurt breakers, A manufacturer of 40 amp fuscs wants to make surc that the mcan ampcragc at which its fuses burn out is In fact 40, If the mean ampcrage is lower than 10, customers will complain because the tuses require replacement too often. It the mean amperage is higher than 10, the manutacturer might be liable tor damage to an electrical system due to fuse malfunction. To verity the amperage ef the fuscs, 3 samplc of fuscs is to be sclected and inspected. If a hypothcsis test were to bc performed on the resulting data, what null and alternative hypothescs would be of interest to the manufacturer? H0: > 40 Hai 40 H0: -40 Ha:

Explanation / Answer

a)

H0: = 40

Ha: 40

b)

A type I error would be declaring a fuse as being defective when in fact there is nothing wrong with the fuse.

c)

A type II error would be declaring a fuse to be satisfactory when in fact it is defective.

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