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A manufacturer of electronic components is testing the durability of a newly designed
Chapter 12, Problem AP4.37(choose chapter or problem)
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 H0 : m = 58 and Ha : m > 58. The P-value for the resulting onesample 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 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 lower than the mean for the earlier model is 0.035. Questions AP4.38 and AP4.39 refer to the following situation. Do childrens fear levels change over time and, if so, in what ways? Little research has been done on the prevalence and persistence of fears in children. Several years ago, two researchers surveyed a randomly selected group of 94 thirdand fourth-grade children, asking them to rate their level of fearfulness about a variety of situations. Two years later, the children again completed the same survey. The researchers computed the overall fear rating for each child in both years and were interested in the relationship between these ratings. They then assumed that the true regression line was mlater rating = a + b (initial rating) and that the assumptions for regression inference were satisfied. This model was fitted to the data using least-squares regression. The following results were obtained from statistical software. AP4
Questions & Answers
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 H0 : m = 58 and Ha : m > 58. The P-value for the resulting onesample 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 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 lower than the mean for the earlier model is 0.035. Questions AP4.38 and AP4.39 refer to the following situation. Do childrens fear levels change over time and, if so, in what ways? Little research has been done on the prevalence and persistence of fears in children. Several years ago, two researchers surveyed a randomly selected group of 94 thirdand fourth-grade children, asking them to rate their level of fearfulness about a variety of situations. Two years later, the children again completed the same survey. The researchers computed the overall fear rating for each child in both years and were interested in the relationship between these ratings. They then assumed that the true regression line was mlater rating = a + b (initial rating) and that the assumptions for regression inference were satisfied. This model was fitted to the data using least-squares regression. The following results were obtained from statistical software. AP4
ANSWER:Step 1 of 2
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.