Question 8: A machine at AMT & Co. fills120-ounce jugs with laundry softener.
A quality control inspector wishes to test if the machineunderfills the jugs or not. Assume
the distribution of the amount of laundry softener in these jugs isNormal. Under “standardâ€
circumstances, the mean amount should be 120 ounces with a standarddeviation of 1 ounce.
a. (2 mark) What are the hypotheses the quality control inspectorwishes to test?
b. Suppose the quality control inspector wishes toconduct the test using α = 0.10
and a sample size of 40. What is the range of values of Ì„x forwhich he will accept H0?
c. Suppose the quality control inspector wishes toconduct the test using α = 0.10
and a sample size of 40. If the true mean amount of detergent inthese jugs is 119.5 ounces,
what is the power of the test?
d. If the observed sample mean amount in the simplerandom sample of 40 jugs
equals 119.62 ounces, find the P-value.
