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.

a) Concluding that the garbage collector picks up on average more than 4 tons of garbage per day when,

in fact, he doesn’t.

b) Not concluding that the garbage collector picks up on average more than 4 tons of garbage per day

when, in fact, he does.

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

picks up more.

d) Not concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact,

he does.

I'm confused with the wording but my guess is between B and C

The correct option is (c).

Step-by-step explanation:

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.  

β = Probability of accepting H₀ when H₀ is false.

In this case we need to test the hypothesis whether the garbage collector's belief is true or not.

The hypothesis can be defined as:

H₀: The garbage collector averages picking up four tons of garbage per day, i.e. μ = 4.

Hₐ: The garbage collector averages picking up more than four tons of garbage per day, i.e. μ > 4.

Consider that the garbage collector made a type II error while drawing the conclusions of the test.

This implies that the garbage collector failed to reject the null hypothesis incorrectly.

That is, he concluded that the he picks up on average four tons of garbage per day, when in fact he picks up more than four tons of garbage every day.

Thus, the correct option is (c).

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