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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-by-side 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 Table?1.5 (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: HYPERLINK "javascript:ShowFootnote('1_28',true)" 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. ................
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