Question

Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of less than 5 days." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's alternative hypothesis is:______

a. μ > 5
b. σ > 5
c. n = 60
d. μ < 5
e. μ = 5

Answer 1

Null hypothesis:
`\mu \geq 5`

The null hypothesis can be on this way:
`\mu=5`, but is better put the complement of the alternative hypothesis.

Alternative hypothesis:
`\mu < 5`

So the best answer for this case would be:

d. μ < 5

Explanation:

Previous concepts

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 is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "if the mean processing time is less than 5 days.". So we want to check if the population mean is less than 5 days, so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:
`\mu \geq 5`

The null hypothesis can be on this way:
`\mu=5`, but is better put the complement of the alternative hypothesis.

Alternative hypothesis:
`\mu< 5`

So the best answer for this case would be:

d. μ < 5