Question

A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

H0: \mu \leq 5 days versus H1: \mu > 5 days. At \alpha = .05, choose the right option.
a) Reject H0 if tcalc < 1.7960
b) Reject H0 if tcalc >1.7960

Answer 1

The degrees of freedom first given by:

`df=n-1=12-1=11`

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

`t_(\alpha)= 1.796`

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :

Null hypothesis:
`\mu \leq 5`

Alternative hypothesis:
`\mu > 5`

The statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

The degrees of freedom first given by:

`df=n-1=12-1=11`

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

`t_(\alpha)= 1.796`

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960