Question

An individual can take either a scenic route to work or a nonscenic route. She decides that use of the nonscenic route canbe justified only if it reduces the mean travel time by more than 10 minutes.a. If u 1 is the mean for the scenic route and u 2 for the nonscenic route. what hypotheses should be tested?b. If u 1 is the mean for the nonscenic route and u Zfor the scenic route, what hypotheses should be tested?

Answer 1

a) Null hypothesis:
`\mu_2 -\mu_1 \geq 10`

Alternative hypothesis:
`\mu_2 -\mu_1 <10`

b) Null hypothesis:
`\mu_1 -\mu_2 \geq 10`

Alternative hypothesis:
`\mu_1 -\mu_2 <10`

Explanation:

Previous concepts and notation

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Part a

The notation for this case is:

`\mu_1` mean for the scenic route

`\mu_2` mean for the non scenic route

The claim that we want to test is: "She decides that use of the nonscenic route can be justified only if it reduces the mean travel time by more than 10 minutes." and this needs to be on the alternative hypothesis.

So the correct system of hypothesis would be:

Null hypothesis:
`\mu_2 -\mu_1 \geq 10`

Alternative hypothesis:
`\mu_2 -\mu_1 <10`

Part b

The notation for this case is:

`\mu_2` mean for the scenic route

`\mu_1` mean for the non scenic route

The claim that we want to test is: "She decides that use of the nonscenic route can be justified only if it reduces the mean travel time by more than 10 minutes." and this needs to be on the alternative hypothesis.

So the correct system of hypothesis would be:

Null hypothesis:
`\mu_1 -\mu_2 \geq 10`

Alternative hypothesis:
`\mu_1 -\mu_2 <10`