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Chapter 12: Q. 1 (page 759)

Oil and residuals Exercise 59 on page 193 (Chapter 3) examined data on the depth of small defects in the Trans-Alaska Oil Pipeline. Researchers compared the results of measurements on 100 defects made in the field with measurements of the same defects made in the laboratory. The figure below shows a residual plot for the least-squares regression line based on these data. Are the conditions for performing inference about the slope尾 of the population regression line met? Justify your answer.

Short Answer

Expert verified

The equal variance requirement has not been met.

Step by step solution

01

Given Information

Need to find which variance requirements have not been met.

02

Explanation

There are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random

The Equal variance requirement has not been met, because the vertical spread is larger to the right than it is to the left in the residual plot.

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Most popular questions from this chapter

Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of 20Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber 12inches by 12inches by 1inch.) A scatterplot of the data is shown below

(a) Some computer output and a residual plot from a least squares regression on these data appear below. Explain why a linear model may not be appropriate in this case.

(B) Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter 30inches. Show your work.

(c) Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.

A distribution of exam scores has mean 60and standard deviation 18. If each score is doubled, and then 5is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores?

(a) mean=115and standard deviation=31

(b) mean=115and standard deviation=36

(c) mean=120and standard deviation=6

(d) mean=120and standard deviation=31

(e) mean=120 and standard deviation=36

The slope 尾 of the population regression line describes

(a) the exact increase in the selling price of an individual unit when its appraised value increases by \(1000

(b) the average increase in the appraised value in a population of units when the selling price increases by \)51000.

(c) the average increase in selling price in a population of units when the appraised value increases by \( 1000.

(d) the average selling price in a population of units when a unit's appraised value is 0.

(e) the average increase in appraised value in a sample of 16 units when the selling price increases by \) 1000.

An experimenter wishes to test whether or not two types of fish food (a standard fish food and a new product) work equally well at producing fish of equal weight after a two-month feeding program. The experimenter has two identical fish tanks (1 and 2) to put fish in and is considering how to assign 40fish, each of which has a numbered tag, to the tanks. The best way to do this would be to

(a) put all the odd-numbered fish in one tank, the even in the other, and give the standard food type to the odd-numbered ones.

(b) obtain pairs of fish whose weights are virtually equal at the start of the experiment and randomly assign one to Tank 1 and the other to Tank2, with the feed assigned at random to the tanks.

(c) proceed as in part (b), but put the heavier of the pair into Tank2.

(d) assign the fish at random to the two tanks and give the standard feed to Tank1.

(e) not proceed as in part (b) because using the initial weight in part (b) is a nonrandom process. Use the initial length of the fish instead.

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.
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