A manufacturer of salad dressings uses machines to dispense

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate the p-value.

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=8 (i.e. null hypothesis)

Ha: mu not equal to 8 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(7.983-8)/(0.15/sqrt(48))

=-0.79

It is a two-tailed test.

So the p-value= 2*P(Z<-0.79) =0.4296 (from standard noraml table)