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Chapter 12: Q. 37 (page 805)

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 58months. The company takes a simple random sample of 120integrated 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" H0:渭=5858 and Ha:渭>58The P-value for the resulting one-samplet-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 is0.035.

Short Answer

Expert verified

(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

01

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.

02

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 is0.035.

03

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 is0.035.

04

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.

05

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 is0.035.

06

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.

07

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 is0.035.

08

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.

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Which of the following statements about the t distribution with degrees of freedom df is (are) true?

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