Question

Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 30-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 30. If the mean amperage is lower than 30, customers will complain because the fuses require replacement too often. If the mean amperage is higher than 30, the manufacturer might be liable for damage to an electrical system as a result of fuse malfunction. To verify the mean amperage of the fuses, a sample of fuses is selected and tested. If a hypothesis test is performed using the resulting data, what null and alternative hypotheses would be of interest to the manufacturer?

H0: μ = 30 versus Ha: μ 29

H0: μ = 30 versus Ha: μ 30

H0: μ = 30 versus Ha: μ > 30

H0: μ = 30 versus Ha: μ < 31

H0: μ = 30 versus Ha: μ < 30

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 30
Alternative hypothesis: u $\neq$ 30

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.