Chapter 10.2, Problem 1.4CYU

To determine

To find: Whether using the previous problem, it could be said that the total difference in the mean amount of the liquid that has been dispensed was 12 ounces.

Answer to Problem 1.4CYU

No, because the probability is too low.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left({\overline{x}}_1\right)=27\\ \text{Sample mean}\left({\overline{x}}_2\right)=17\\ \text{Standard deviation}\left({\sigma }_1\right)=0.8\\ \text{Standard deviation}\left({\sigma }_2\right)=0.5\end{array}$

  $P\left({\overline{x}}_1-{\overline{x}}_2>12\right)=0$

Calculation:

The obtained probability of difference is 0 which is too small. Thus, it is impossible to say that the total difference in the mean amount of the liquid that has been dispensed was 12 ounces.