Define simple random sampling. Describe briefly one difficulty associated with simple random sampling.
Freeze-drying is an economically important process used in the production of coffee. It improves the retention of the volatile aroma compounds. In order to maintain the quality of the coffee, technologists need to monitor the drying rate, measured in suitable units, at regular intervals. It is known that, for best results, the mean drying rate should be 70.3 units and anything substantially less than this would be detrimental to the coffee. Recently, a random sample of 12 observations of the drying rate was as follows.
$$\begin{array} { l l l l l l l l l l l l }
66.0 & 66.1 & 59.8 & 64.0 & 70.9 & 71.4 & 66.9 & 76.2 & 65.2 & 67.9 & 69.2 & 68.5
\end{array}$$
Carry out a test to investigate at the \(5 \%\) level of significance whether the mean drying rate appears to be less than 70.3. State the distributional assumption that is required for this test.
Find a 95\% confidence interval for the true mean drying rate.