Question

multiple choice 4 points
identify the type ii error.
a waste management service attempts to design routes so that each of their trucks pick - up on average four tons of garbage or less. a garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test.
identify a type ii error in the context of this hypothesis test.
concluding that the garbage collector picks up on average more than 4 tons of garbage per day when, in fact, he doesnt
not concluding that the garbage collector picks up on average more than 4 tons of garbage per day when, in fact, he does
concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he picks up more
not concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he does
multiple choice 4 points
assume a normal distribution and use a hypothesis test to test the given claim.

Explanation:

A Type II error occurs when we fail to reject a false null hypothesis. In hypothesis testing, the null hypothesis \(H_0\) is the statement being tested, and the alternative hypothesis \(H_1\) is the statement we are trying to find evidence for. In this context, the null hypothesis would likely be that the garbage collector picks up 4 tons or less (\(H_0:\mu\leq4\)) and the alternative \(H_1:\mu > 4\). A Type II error means we conclude that the garbage collector does not pick up more than 4 tons (fail to reject \(H_0\)) when in reality, he does pick up more than 4 tons.

Answer:

Concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he picks up more.