A gum manufacturer claims that on average the flavor of an entire packet of its gum would last for more than 39 minutes. A quality controller selects a random sample of 55 packets of gum. She finds the average time for which the gum flavor lasts is 40 minutes with a standard deviation of 5.67 minutes.

a. Formulate a hypothesis test to validate the manufacturer’s claim.

b. After a new technique to improve the lasting period of the gum flavor was applied, the quality controller reselected 60 packets of gum and found that the average time for which the gumflavor lasts is 45 minutes with a standard deviation of 3.15 minutes. Is there sufficient evidence to conclude that the new technique significantly increased the lasting time?

c. Use a 95% confidence interval for the population average time for which the flavor lasts to validate the manufacturer’s claim after the new technique is applied.