2 When it is operating properly a chemical plant has a mean

2. When it is operating properly, a chemical plant has a mean daily production of at least 740 tons. The output is measured on a simple random sample of 60 days. The sample had a mean of 715 tons/day and a standard deviation of 24 tons/day. Let u represent the mean daily output of the plant. An engineer tests H0: mu > = 740 versus H1: mu

Solution

2)a)

n =60 , sample mean =715 , SD = 24

z = (X - X(mean)) / ( SD/sqrt(n))

= ( 715- 740)/( 24 / sqrt(60) )

= -8.068

Therefore P-value = 1- (~1) = 0 Answer

b)

It would be highly unusual for the plant to be operating properly since the probability of the sample mean being 715 when the true mean is 740 is nearly 0.