A manufacturer of electronic components is testing the durability of a newly designed integrated circuit to determine whether its life span is longer than that of the earlier model, which has a mean life span of $58$months. The company takes a simple random sample of $120$integrated circuits and simulates normal use until they stop working. The null and alternative hypotheses used for the significance test are given by role="math" localid="1650625928506" $H_0:\mu =58$58 and $H_a:\mu >58$The P-value for the resulting one-sample$t$-test is $0.035$. Which of the following best describes what the P-value measures

(a) The probability that the new integrated circuit has the same life span as the current model is $0.035$.

b) The probability that the test correctly rejects the null hypothesis in favor of the alternative hypothesis is $0.035$.

(c) The probability that a single new integrated circuit will not last as long as one of the earlier circuits is $0.035$.

(d) The probability of getting a sample statistic as far or farther from the null value if there really is no difference between the new and the old circuits is$0.035$.

We need to find the probability that the new integrated circuit has the same life span as the current model is $0.035$.

By observing the above conclusion the given option does not fit according to question the probability that the new integrated circuit has the same life span as the current model is$0.035$.

We need to find the probability that the test correctly rejects the null hypothesis in favor of the alternative hypothesis is$0.035$.

By observing the above conclusion the given option does not fit according to question the probability that the test correctly rejects the null hypothesis in favor of the alternative hypothesis is $0.035$.

We need to find the probability that a single new integrated circuit will not last as long as one of the earlier circuits is$0.035$.

By observing the above conclusion the given option does not fit according to the question the probability that a single new integrated circuit will not last as long as one of the earlier circuits is $0.035$.

We need to find the probability of getting a sample statistic as far or farther from the null value if there really is no difference between the new and the old circuits is$0.035$.

The P-value measures the probability of getting the same value or a more extreme value as the null value if there really is no difference between the circuits and then (d) is the correct answer.