Answer:
The t-statistic is t=0.631.
Step-by-step explanation:
We have to perform an hypothesis test on the mean.
The claim is that the new method performs different from the actual method.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=12. The sample mean is 10.2 hours and the sample standard deviation is 1.1.
As the population standard deviation is not known, we will estimate it from the sample standard deviation and use a t-statistic.
The degrees of freedom are:
The t-statistic is:
The P-value of this two-tailed test, with t=0.631 and df=11, is
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis failed to be rejected.