Question

The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation. Which of the following is the correct set of hypotheses?

H0:μ=10.6Ha:μ>10.6 A

H0:μ=10.6Ha:μ≠10.6 B

H0:μ=10.6Ha:μ<10.6 C

H0:μ=12.9Ha:μ≠12.9 D

H0:μ=12.9Ha:μ<12.9 E

Answer 1

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis:
`\mu =10.6`

Alternative hypothesis:
`\mu \\eq 10.6`

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

Explanation:

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis:
`\mu =10.6`

Alternative hypothesis:
`\mu \\eq 10.6`

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

And the data from the sample is:

`\bar X = 12.9` represent the sample mean

`n =40` the sample size