Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.
The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?
I. Take the square root of the number of Cheerios.
II. Cube the number of Cheerios.
III. Take the log of the number of Cheerios.
IV. Take the log of the diameter.
(a) I and II
(b) I and III
(c) II and III
(d) II and IV
(e) I and IV
The single transformation that is reasonable for them to try is option (b) I and III.
The given data is
The scatterplot pattern suggests that a power model might be appropriate.
A power model uses the response variable's root or logarithm.
Cheerios is the response variable, thus we should try transformations I and III.
A random sample of students at a very large university was asked which social-networking site they used most often during a typical week. Their responses are shown in the table below.
Assuming that gender and preferred networking site are independent, which of the following is the expected count for female and LinkedIn?
Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value of x, the population of y-values is Normally distributed.
(b) The standard deviation of the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x. (c) The sample size—that is, the number of paired observations (x, y)—exceeds .
(d) There exists a straight line such that, for each value of x, the mean of the corresponding population of y-values lies on that straight line.
(e) The data come from a random sample or a randomized experiment.
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 of the population regression line met? Justify your answer.
Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the University of Washington student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.
From the chi-square test performed in this study, we may conclude that
(a) there is convincing evidence of an association between the gender of an individual participating in the event and development of a rash.
(b) mud wrestling causes a rash, especially for women.
(c) there is absolutely no evidence of any relation between the gender of an individual participating in the event and the subsequent development of a rash.
(d) development of a rash is a real possibility if you participate in mud wrestling, especially if you do so on a regular basis.
(e) the gender of the individual participating in the event and the development of a rash are independent.
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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