Question

AP4.37 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 typical use until they stop working. The null and alternative hypotheses used for the significance test are $H0:\mu =58$ and

$Ha:\mu >58$. 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 mean as far or farther above 58 if there really is no difference between the new and the old circuits is 0.035.
e. The probability of getting a sample mean for the new integrated circuit that is less than the mean for the earlier model is 0.035.

Short answer

The correct answer is option (d) The probability of getting a sample mean as far or farther above $58$ if there really is no difference between the new and the old circuits is $0.035$.

Step-by-step solution

Given information

To find out the best describes what the $P$ -value measures.

Explanation

The p-value is a number produced from a statistical test that reflects how likely it is that you would have discovered a specific collection of observations if the null hypothesis were true.
In analysis of data, P-values are used to evaluate if the null hypothesis will be rejected.
In this investigation, an electronics component maker is evaluating the durability of a newly developed integrated circuit to see if it has a longer life cycle than the previous model.
Knowing that the P-value measures the probability of getting the same or a more extreme value as the null value, option (d) is accurate if there is no difference between the circuits.

As a result, option (d) is correct.