Reconsider the investigation of the manufacturing process that is producing hypodermic needles. Using the data from the most recent sample of needles, a 90% confidence interval for the average diameter of needles is found to be (1.62 mm, 1.66 mm). For each of the following statements, say whether VALID or INVALID.

a. We are 90% confident that the average diameter of the sample of 35 needles is between 1.62 and 1.66 mm.

b. Based on the 90% confidence interval, there is evidence that the average diameter of needles produced by this manufacturing process is 1.65 mm.

c. Based on the 90% confidence interval, there is evidence that the average diameter of needles produced by this manufacturing process is different from 1.65 mm.

d. We are 90% confident that the average diameter of needles produced by this manufacturing process is between 1.62 and 1.66 mm.

e. About 90% of the needles produced by this manufacturing process have a diameter between 1.62 and 1.66 mm.

f. If we want to be more than 90% confident, we should take a larger sample of needles.