Ranking driving performance of professional golfers. Refer to The Sport Journal (Winter 2007) analysis of anew method for ranking the total driving performance ofgolfers on the PGA tour, Exercise 2.52 (p. 97). Recall thatthe method uses both the average driving distance (yards)and driving accuracy (percent of drives that land in thefairway). Data on these two variables for the top 40 PGAgolfers are saved in the accompanying file. A professionalgolfer is practicing a new swing to increase his averagedriving distance. However, he is concerned that his drivingaccuracy will be lower. Is his concern a valid one? Explain.
Yes, his concern is valid.
To answer the question, we will first have to check whether there is any relation between the driving distance and the driving accuracy. Therefore we will first construct a scatterplot using the data given for the two variables.
The data for the two variables is as follows:
The graph is given below:
We can infer from the graph that there is a negative correlation between driving distance and driving accuracy. It is observed that for golfers who had a lengthy driving distance, their driving accuracy was low.
Therefore, the concern of the professional golfer who is trying to increase his driving distance is valid. If he tries to increase his driving distance, his accuracy will reduce.
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.5 (p. 72). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The number of wheels on each of the 28 robots is listed in the accompanying table.
(4 4 3 3 3 6 4 2 2 2 1 3 3 3 3 4 4 3 2 8 2 2 3 4 3 3 4 2)
Source: Based on S. Chew et al., “Do Social Robots Walk or Roll?” International Conference on Social Robotics, Vol. 6414, 2010 (adapted from Figure 2).
a. Generate a histogram for the sample data set. Is the distribution of number of wheels mound-shaped and symmetric?
b. Find the mean and standard deviation for the sample data set.
c. Form the interval, xbar ± 2s.
d. According to Chebychev’s Rule, what proportion of sample observations will fall within the interval, part c?
e. According to the Empirical Rule, what proportion of sample observations will fall within the interval, part c?
f. Determine the actual proportion of sample observations that fall within the interval, part c. Even though the histogram, part a, is not perfectly symmetric, does the Empirical Rule provide a good estimate of the proportion?
Land purchase decision. A buyer for a lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the buyer will purchase the land; otherwise, he won’t. The owner of the land reports that the height of the trees has a mean of 30 feet and a standard deviation of 3 feet. Based on this information, what is the buyer’s decision?
Consider the following sample of five measurements: 2, 1, 1, 0, 3.
a. Calculate the range, s2, and s.
b. Add 3 to each measurement and repeat part a.
c. Subtract 4 from each measurement and repeat part a.
d. Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?
Question: Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011) study on the sustainability
behaviors of CPA corporations, Exercise 2.48 (p. 96). Numerical measures of variation for level of support for the 992 senior managers are shown in the accompanying Minitab printout.
Descriptive Statistics: Support
a. Locate the range on the printout. Comment on the accuracy of the statement: “The difference between the largest and smallest values of level of support for the 992 senior managers is 155 points.”
b. Locate the variance on the printout. Comment on the accuracy of the statement: “On average, the level of support for corporate sustainability for the 992 senior managers is 722 points.”
c. Locate the standard deviation on the printout. Does the distribution of support levels for the 992 senior managers have more or less variation than another distribution with a standard deviation of 50? Explain.
d. Which measure of variation best describes the distribution of 992 support levels? Explain.
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample were randomly divided into three groups: those who received a dosage of over-the-counter cough medicine (DM), those who received a dosage of honey (H), and those who received no dosage (control group). The coughing improvement scores (as determined by the children’s parents) for the patients are reproduced in the next table.
12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12
4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10
No Dosage (Control)
13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3
a) Find the median improvement score for the honey dosage group.
b) Find the median improvement score for the DM dosage group.
c) Find the median improvement score for the control group.
d) Based on the results, parts a–c, what conclusions can pediatric researchers draw? (We show how to support these conclusions with a measure of reliability in subsequent chapters.)
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