Answer:
There is no evidence to said that the technique performs differently than the traditional method.
Step-by-step explanation:
First, we need to write the null and alternative hypothesis as:
H0: x = 11.7
H1: x ≠ 11.7
Where x is the population mean for the new method.
Taking into account that the population distribution is approximately normal and the standard deviation of the population is unknown, we can calculated the statistic as:
Where t follows a distribution t-student with n-1 degrees of freedom.
So, replacing x' by the mean of the sample, s by the standard deviation of the sample and n by the size of the sample, we get:
Then, we can find the critical points as:
P(t<t1) = 0.025
P(t<t2) = 0.975
So, with 22 degrees of freedom, the critical point t1 and t2 are equal to -2.07 and 2.07 respectively.
Since 1.37 is between the critical points, we can't reject H0. it means that there is no evidence to said that the technique performs differently than the traditional method.