Homework 1

Chapter 1 Problems

1.23 Medical students. Students who have finished medical school are assigned to residencies in hospitals to receive further training in a medical specialty. Here is part of a hypothetical data base of students seeking residency positions. USMLE is the student’s score on Step 1 of the national medical licensing examination.

1. What individuals does this data set describe?
2. In addition to the student’s name, how many variables does the data set contain? Which of these variables are categorical and which are quantitative?

1.24 Buying a refridgerator. 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?

1.35 Where are the nurses? The following spreadsheet gives the number of active nurses per 100,000 people in each state. NURSES

1. 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?
   
2. 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 the time to complete the task recorded. Her are the improvements (before \(-\) after) times in seconds after four weeks for the two groups: NINTENDO

1. In the context of this study, what do the negative values in the data set mean?
2. 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 from 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 be 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.

3. 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.)

Chapter 2 Problems

2.25 Incomes of college grads. According to the Census Bureau’s Current Population Survey, the mean and median 2012 income of people at least 25 years old who had a bachelor’s degree but no higher degree were $50,281 and $62,597. Which of these numbers is the mean and which is the median? Explain your reasoning.

2.26 Saving for retirement. Retirement seems a long way off, and we need money now, so saving for retirement is hard. Once every three years, the Board of Governors of the Federal Reserve System collect data on household assets and liabilities through the Survey of Consumer Finances (SCF). The most recent such survey was conducted in 2010, and the survey results were released to the public in April 2013. The survey presents data on retirement assets, which include defined contribution and Individual Retirement Account (IRA) balances. For married households the mean value per household is $123,968, but the median value is just $10,000. For single households, the mean is $33,585, and the median is $0. What explains the differences between the two measures of center, both for married and single households? What does the median of $0 say about the percentage of single households with retirement assets?