Stat 216 Excel/PHStat Homework Assignment #1 Please visit www.stat.wmich.edu/s216/phstat.html to learn how to start up Excel/PHStat. Tip: Read through this entire assignment before getting onto a computer. The data that you will need for this assignment can be found in the worksheet called cars. The worksheet contains on 80 different kinds of cars. From Motor Trend Car, we see that the variables include MPG, CYL (4, 6, 8), DISP (size), HP, DRAT, WT, QSEC, VS (=0, =1), AM, GEAR (3, 4, 5), and CARB (0, 2, 4, 6, 8). You will be obtaining a subset of this data. Every student will have a different data set. Directions for obtaining your unique data subset: • Go to www.stat.wmich.edu/s216/info.html and click on Winter 2002 link and HW Data link. • Choose Cars from the list of data sets. • Click on the Submit button. • Put check marks next to all the variables under Select variable(s) to be resampled. • Enter 50 for Sample size. • Enter the last four digits of your student ID for the PIN Number. • Click on the Submit button. • Follow the instructions on the page that comes up on your browser, which will tell you to click on the link provided. A text file containing the data will come up next, which you should download. Use a floppy diskette if you are on a lab PC. • Next, open the file into Excel. Choose Text files under Files of type. • Choose Delimited for the Text Import Wizard step 1. • Choose Comma for step 2. “Un-choose” Tab. • Everything should appear to line up. Leave Column data format as General for step 3. Click Finish. 1) Obtain the descriptive statistics for MPG, HP, and WT. In your report, include the table output by Excel, and make an additional table listing these particular measures of central tendency: mean, median, mode, and midrange. Also list these measures of variation in your table: range, variance, standard deviation, and coefficient of variation. Note: A couple of these measures (midrange and CV) will require you to make some small additional calculations by hand. 2) Get a stem-and-leaf plot of DISP. Determine the mode of this data set from the plot. 3) Obtain a histogram of WT by following these instructions: Add another column to the spreadsheet, say in column “o.” Name it “Class boundaries,” if you wish. Enter in the following numbers: 1.999, 2.499, 2.999, 3.499, 3.999, 4.499, 4.999, 5.499. Specify this range of cells for the “Bin range” part of the histogram dialog box. Note: The default histogram is a very poor graph, which makes these modifications necessary. Details of these modifications are on pages 80-83 of the textbook, but all you really need to do is the following (before you copy it into Word): • Remove the gaps between the bars in the histogram (see top of page 83). • Resize the graph in order to make it more readable like so: Select the graph by left- clicking close to the edge of the white area surrounding the histogram. Now position the mouse pointer over the bottom left corner. Resize the graph by dragging it down and to the right into a more “square” shape. Based on the histogram, what is the shape of the data? 4. Get a boxplot of MPG (and check the box next to Five-number Summary). What is the shape? Does this agree with the shape you reported in #3. Remember that tilting your head to the left or turning the printout 90 degrees clock-wise helps you determine skewness direction, if any. 5. Using the five-number summary obtained above, what are the quartiles? Calculate the midhinge and interquartile range (IQR) as well. For the last problem, you will not need your subset of data. 6. Suppose the full data set is representative of all cars. Imagine that we are interested in the probability of a car being coded vs = 0, as opposed to vs = 1. Since 50 of the 80 cars in the full data set are coded vs = 0, 50/80 = 0.625 would be a good estimate of this probability. Now suppose we take a sample of 20 cars. Use Excel/PHStat to get the binomial probabilities for the possible outcomes. a. Is this a valid binomial situation? Are all the assumptions met? b. How many vs = 0 would we “expect” to find in this sample? c. What is the probability of finding exactly 9 cars coded vs = 0 in this sample? d. What is the probability of finding between 8 and 14 (inclusive) cars coded vs = 0 in this sample? e. What is the probability of finding at least 11 cars coded vs = 0 in this sample? f. What is the probability of finding 15 or more cars coded vs = 0 in this sample? g. What is the probability of finding at most 11 cars coded vs = 0 in this sample? Note: You are expected to incorporate all graphs and descriptive output into a Word (or other suitable word processor) document, along with all of your answers. Be sure that you answer all parts of the questions. Feel free to use a pen or pencil for some parts, like determining the midhinge and IQR in #5. Just make sure your leave room on the page for such hand calculations before printing your Word document. Tip on copying plots from Excel to Word: Stem-and-leaf plots: Select the plot area on the spreadsheet by highlighting the appropriate cell range. Copy and past in Word. Histograms: Select the plot by clicking on the white chart area. Copy and paste in Word. Boxplots: Copy and paste into Word. It will be very large initially, so reduce the plot like so: Select the graph, then choose Object under the Format menu. Select the Position tab, then unclick Float over text. Now click on the Size tab. Under Scale, reduce the Height and Weight to 40% or so. Click OK..