1.24 Buying a refrigerator. Consumer Reports will have an article comparing
refrigerators in the next issue. Some of the characteristics to be included in the
report are the brand name and model; whether it has a top, bottom, or side-byside freezer; the estimated energy consumption per year (kilowatts); whether or
not it is Energy Star compliant; the width, depth, and height in inches; and both
the freezer and refrigerator net capacity in cubic feet. Which of these variables
are categorical, and which are quantitative? Give the units for the quantitative
variables and the categories for the categorical variables. What are the individuals
in the report?
1.26 Facebook, Twitter, and LinkedIn users. After years of explosive
growth in number of users of social networking sites in all age ranges and
demographics, it is hard to argue that social media haven’t changed forever how
we interact and connect online. Although Facebook is still the dominant player in
social networking, both Twitter and LinkedIn have continued to increase their
usage. Here is the age distribution of the users for the three sites in 2013:17
(a)Draw a bar graph for the age distribution of Facebook users. The leftmost bar
should correspond to “13 to 17,” the next bar to “18 to 24,” and so on. Do the same
for Twitter and LinkedIn, using the same scale for the percent axis.
(b)Describe the most important difference in the age distribution of the audience
for these three social networking sites. How does this difference show up in the bar
graphs? Do you think it was important to order the bars by age to make the
comparison easier? Why or why not?
(c)Explain why it is appropriate to use a pie chart to display any of these
distributions. Draw a pie chart for each distribution. Do you think it is easier to
compare the three distributions with bar graphs or pie charts? Explain your
reasoning.
1.35 Where are the nurses? Table 1.5 gives the number of active nurses per
100,000 people in each state.25
(a)Why is the number of nurses per 100,000 people a better measure of the
availability of nurses than a simple count of the number of nurses in a state?
(b)Make a histogram that displays the distribution of nurses per 100,000 people.
Write a brief description of the distribution. Are there any outliers? If so, can you
explain them?
1.38 Nintendo and laparoscopic skills. In laparoscopic surgery, a video
camera and several thin instruments are inserted into the patient’s abdominal
cavity. The surgeon uses the image from the video camera positioned inside the
patient’s body to perform the procedure by manipulating the instruments that have
been inserted. It has been found that the Nintendo Wii™ reproduces the
movements required in laparoscopic surgery more closely than other video games
with its motion-sensing interface. If training with a Nintendo Wii™ can improve
laparoscopic skills, it can complement the more expensive training on a
laparoscopic simulator. Forty-two medical residents were chosen, and all were
tested on a set of basic laparoscopic skills. Twenty-one were selected at random to
undergo systematic Nintendo Wii™ training for one hour a day, five days a week,
for four weeks. The remaining 21 residents were given no Nintendo Wii™ training
and asked to refrain from video games during this period. At the end of four weeks,
all 42 residents were tested again on the same set of laparoscopic skills. One of the
skills involved a virtual gall bladder removal, with several performance measures
including time to complete the task recorded. Here are the improvement (before —
after) times in seconds after four weeks for the two groups:28
(a)In the context of this study, what do the negative values in the data set mean?
Back-to-back stemplots back-to-back stemplots can be used to compare the
two samples. That is, use one set of stems with two sets of leaves, one to the right
and one to the left of the stems. (Draw a line on either side of the stems to separate
stems and leaves.) Order both sets of leaves from smallest at the stem to largest
away from the stem. Complete the back-to-back stemplot started below. The data
have been rounded to the nearest 10, with stems being 100s and leaves being 10s.
The stems have been split. The first control observation corresponds to —80 and
the next two to —30 and —10.
(c)Report the approximate midpoints of both groups. Does it appear that the
treatment has resulted in a greater improvement in times than seen in the control
group? (To better understand the magnitude of the improvements, note that the
median time to complete the task on the first occasion was 11 minutes and 40
seconds, using the times of all 42 residents.)
1.45 Ozone hole. The ozone hole is a region in the stratosphere over the
Antarctic with exceptionally depleted ozone. The size of the hole is not constant
over the year but is largest at the beginning of the Southern Hemisphere spring
(August–October). The increase in the size of the ozone hole led to the Montreal
Protocol in 1987, an international treaty designed to protect the ozone layer by
phasing out the production of substances, such as chlorofluorocarbons (CFCs),
believed to be responsible for ozone depletion. The following table gives the
average ozone hole size for the period September 7 to October 13 for each of the
years from 1979 through 2013 (note that no data were acquired in 1995).33 To get a
better feel for the magnitude of the numbers, the area of North America is
approximately 24.5 million square kilometers (km2).
The two parts of this exercise will have you draw two graphs of these data.
(a)First make a time plot of the data. The severity of the ozone hole will vary from
year to year depending on the meteorology of the atmosphere above Antarctica.
Does the time plot illustrate only year-to-year variation or are other patterns
apparent? Specifically, is there a trend over any period of years? What about
cyclical fluctuation? Explain in words the change in the average size of the ozone
hole over this 35-year period.
(b)Now make a stemplot of the data. What is the midpoint of the distribution of
ozone hole size? Do you think that the stemplot and the midpoint are a good
description of this data set? Is there important information in the time plot that is
not contained in the stemplot? When data are collected over time, you should
always make a time plot.