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Chapter 12: Q. 2.2 (page 755)

The previous Check Your Understanding (page 750) described some results from a study of body weights and backpack weights. Here, again, is the Minitab output from the least-squares regression analysis for these data.

2. Would a 99 % confidence interval for the slope β of the population regression line include 0? Justify your answer. (You don't need to do any calculations to answer this question.)

Short Answer

Expert verified

99 % confidence interval for the slope β of the population regression line will include zero in it.

Step by step solution

01

Given Information

It is given in the output that:

n=8

b=0.09080

SEb=0.02831

02

Explanation

The degrees of freedom is the sample size decreased by 2 :

df=n-28-2=6

Thus, if we will carry out the 99% confidence interval for the slope β of the population regression line, then as it is more than the 95% confidence interval for the slope of the population regression line then the confidence interval for the 99% will be large than the 95%confidence interval. So, it will have the possibility that it will contain zero in the confidence interval also the sample size is very small. Thus, 99% confidence interval for the slope βof the population regression line will include zero in it.

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Most popular questions from this chapter

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than \(200,000.

(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

Below are boxplots of SAT Critical Reading and Math scores for a randomly selected group of female juniors at a highly competitive suburban school.

Which of the following cannot be justified by the plots shown above?

(a) The maximum Critical Reading score is higher than the maximum Math score.

(b) Critical Reading scores are skewed to the right, whereas Math scores are somewhat skewed to the left.

(c) The median Critical Reading score for females is slightly higher than the median Math score.

(d) There appear to be no outliers in the SAT score distributions.

(e) The mean Critical Reading score and the mean Math score for females are about the same.

The swinging pendulum Mrs. Hanrahan’s precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulum’s length and its period is

period=2πglength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

In the casting of metal parts, molten metal flows through a “gate” into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminium pistons examined a random sample of 12pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process. A scatterplot of the data is shown below

A least-squares regression analysis was performed on the data. Some computer output and a residual plot are shown below. A Normal probability plot of the residuals (not shown) is roughly linear.

Do these data provide convincing evidence of a straight-line relationship between thickness and gate velocity in the population of pistons formed from this alloy of metal? Carry out an appropriate significance test at the α=0.05level.

Ideal proportions Refer to Exercise 10.

(a) What height would you predict for a student with an arm span of 76 inches? Show your work.

(b) About how far off do you expect the prediction in part (a) to be from the student's actual height? Justify your answer.
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