An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The mean lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically significant at the 0.05 level. If, in fact, there is no difference between the mean lifetimes of the new and old designs, the researcher has:

a) committed a type 1 error

b) committed a type 2 error

c) a probability of being correct, which is equal to the P-value

d) a probability of being correct, which is equal to 1-(P-value)