Question

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$0.035$.

Short answer

(d) The probability of getting the same value or a more extreme value as the null value if there really is no difference between the new circuits and old circuits.

Step-by-step solution

Part (a) step 1: Given Information

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

Part (a) step 2: Explanation

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$0.035$.

Part (b) step 1: Given Information

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

Part (b) step 2: Explanation

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 $0.035$.

Part (c) step 1: Given Information

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

Part (c) step 2: Explanation

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 $0.035$.

Part (d) step 1: Given Information

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$0.035$.

Part (d) step 2: Explanation

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.