a. A machine is set to fill a small bottle of 9.0 grams of medicine. A sample of eight

bottles revealed the following amounts (grams) in each bottle.

9.2

8.7

8.9

8.6

8.8

8.5

8.7

9.0

At the 5% level of significance, can we conclude that the mean weight is less than 9.0

grams?

b. According to the local union president, the mean gross income of truck drivers in the

Chattogram port area follows the normal probability distribution with mean of Tk14,000

and a standard deviation Tk 760. A recent investigative reporter for Independent

Television found, for a sample of 120 plumbers, the mean gross income was Tk 15,600.

Is it reasonable to conclude that the mean income is not equal to Tk 14,000?