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.
a) 75.41892 inches.
Need to find What height would you predict for a student with an arm span of 76 inches.
The estimates a and b are given in the column of "Coef":
Replace x by 5 and evaluate:
This means that we predict that the student will be inches tall.
The expected error made when making predictions is given by , which is estimated by s. Thus we expect that the prediction will be off by 1.613 on average.
Beavers and beetles Do beavers benefit beetles? Researchers laid out 23 circular plots, every four meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth so beetles prefer them. If so, more stumps should produce more beetle larvae.
Minitab output for a regression analysis on these data is shown below. Construct and interpret a 99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.
Which of the following statements about the t distribution with degrees of freedom df is (are) true?
I. It is symmetric.
II. It has more variability than the t distribution with degrees of freedom.
III. As df increases, the t distribution approaches the standard Normal distribution.
(a) I only (c) III only (e) I, II, and III
(b) II only (d) I and II
Insurance adjusters are always vigilant about being overcharged for accident repairs. The adjusters suspect that Repair Shop quotes higher estimates than Repair Shop . To check their suspicion,
the adjusters randomly select cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to ﬁx the vehicle. The
estimates are given below in hundreds of dollars.
Assuming that the conditions for inference are reasonably met, which of the following signiﬁcance tests could legitimately be used to determine whether the adjusters’ suspicion is correct?
I. A paired test
II. A two-sample test
III. A t test to see if the slope of the population regression line is .
(a) I only
(b) II only
(c) I and III
(d) II and III
(e) I, II, and III
An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of of the nearly players on the PGA Tour’s world money list are examined. The average number of putts per hole and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.
A confidence interval for the slope of the population regression line is
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