a) Null hypothesis: The filling machine is calibrated properly and fills cans to contain an average of 128 ounces.
Alternative hypothesis: The filling machine is set too high and fills cans to contain an average of more than 128 ounces.
b) If the null hypothesis is true, the sampling distribution has a mean of 128 ounces, a standard deviation of 2 ounces, and follows a normal distribution.
c) The standard score for the data is (128.2 - 128) / (2 / sqrt(25)) = 1.
d) The P-value for this significance test can be found using a one-sample t-test with 24 degrees of freedom (df = n-1). Using a t-distribution table or a calculator, the P-value for a one-tailed test with a t-score of 1 and 24 degrees of freedom is approximately 0.16.
e) Since the P-value is greater than the level of significance (0.05), we do not reject the null hypothesis.
f) The correct final conclusion in the context of the problem is: There is not enough evidence to suggest that the machine is set too high and not calibrated properly.