Manufacturing and Product Development

Vacuumpacked coffee stays fresh longer, but the package tends to be bumpy and unappealing. In a nitrogen-flushed package, all the oxygen is pushed out by heavier nitrogen, producing a smoother, more attractive package that also stays fresh. A machine used to produce a nitrogen-flushed package should dispense 1.6 moles of nitrogen for a 1-pound package of coffee. In a random sample of 23 packings, the sample mean amount of nitrogen dispensed was x^‾ = 1.78 moles. Assume the underlying distribution is normal, with σ = 0.5 moles, and use a = 0.01.

a. Is there any evidence to suggest the machine is malfunctioning?

b. Compute the p value associated with this hypothesis test.