Refer to Exercise 7.12, where, in a pilot process, vertical spirals were cut to produce latex from \(n=8\) trees to yield (in liters) in a week.

26.8     32.5     29.7     24.6     31.5     39.8     26.5     19.9

(a) Conduct a test of hypotheses with the intent of showing that the mean production is less than 36.2. Take \(\alpha=0.01\) and assume a normal population.

(b) Based on your conclusion in part (a), what error could you have made? Explain in the context of the problem.

the problem.

Data From Exercise 7.12

Transcribed Image Text:

7.12 An effective way to tap rubber is to cut a panel in the rubber tree's bark in vertical spirals. In a pilot process, an engineer measures the output of latex from such cuts. Eight cuts on different trees produced latex (in liters) in a week 26.8 32.5 29.7 24.6 31.5 39.8 26.5 19.9 What can the engineer assert with 99% confidence about the maximum error if she uses the sample mean to estimate true mean yield?