Question

Could you please let me know which of the below options is correct?

We analyze whether the true mean discharge of wastewater per hour from an industrial plan exceeds the company claim of 1000 gallons. For the decision in the one-sided test using alpha = 0.05:

a.) If the plant is exceeding the limit, there is only a 5% chance that we will conclude that they are not exceeding the limit.

b.) If we reject H0, the probability that it is actually true is 0.05.

c.) If the plant is not exceeding the limit, but actually mu = 1000, there is only a 5% chance that we will conclude that they are exceeding the limit.

d.) The probability that the sample mean equals exactly the observed value would equal 0.05 if H0 were true.

e.) All of the above.

Answer 1

Answer

We know that when we use alpha level of 0.05, then there is exactly 5% chances of making a type I error, i.e. rejecting the true null hypothesis.

In all cases, alpha level or significance level is always the chances or probability of making type I error in the hypothesis testing.

In this case, type I error would be rejection of null hypothesis (mean or mu = 1000) and concluding that the mean is exceeding the limit.

If we look at the option C, then it is clear that type I error is made in option C

So, we can say that only option C is correct answer for the given case.

All other options are incorrect, only C is correct.