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STATISTICS 101 - Homework 2 Due Friday, February 1, 2002 • Homework is due by 5:00 PM on the due date at your course instructor’s office. You can always hand in your homework at the end of lecture on Friday. • You may talk with others about the homework problems but please write your solutions up independently. • Please answer homework questions in complete sentences. Make sure to staple the pages of your assignment together. Be sure to indicate your lab section letter on your paper. Homework with out the correct lab section will marked as late. • You normally will have an opportunity to get help on homework during lab. Reading: Jan. 21 Jan. 28 - Jan. 25 - Feb. 1 Section 1.2 Sections 2.1, 2.2 Assignment: 1. Read pages 32-42 of the text and do problems 1.32, 1.36, 1.42, and 1.46. 2. On homework 1 the birth weights of 44 babies born at a Brisbane, Australia hospital were given. Eighteen of those babies were girls. Their birth weights, in grams, are given below. 3837 3523 2383 3334 3430 3500 2208 3480 3866 2576 3116 3542 3208 3428 3278 3746 2184 1745 (a) Calculate the mean and median for these data. Comparing these two values, would you say the distribution of weights is skewed left, symmetric, or skewed right? Explain briefly your choice. (b) Calculate a five number summary for these data and use this to construct a box plot. Be sure to include a realistic axis for the box plot. Is the distribution of scores symmetric or skewed? Explain briefly what it is about the shape of this box plot that indicates symmetry or skew. (c) What are the values of the range and the InterQuartile Range (IQR) for these data? (d) Suppose the hospital found out that the scale was not calibrated correctly and each of the reported weights above is 200 grams more than it should be. If we correct for this mistake how would the mean, median, range and IQR change? Hint: Don’t change the data and recalculate the answers. Instead, think about what each measures and how that is affected by subtracting a constant.) 3. Below are the heights (inches) of ten female students chosen at random from those currently enrolled in Stat 101. 67, 65, 69, 64, 63, 65, 64, 66, 66, 71 (a) Calculate the sample median and sample mean for these data. Interpret each of these values within the context of the problem. That is, what does the median (mean) tell you about the height of females in Stat 101? What does the comparison of these values tell you about the skew or symmetry of the distribution of female heights? (b) Compute the standard deviation for these data using the definitional formula: (pg. 38 in the text) s P (X − X̄)2 s= n−1 1 (c) Check your answer in (e) by using one of the following. • the computational formula given below v P u u P 2 ( X)2 u X − n t s= n−1 • a calculator with statistics capabilities • a computer program that calculates standard deviation. 4. (JMP assignment) How faithful is the Old Faithful Geyser in Yellowstone National Park? In the table below are the times (minutes) between eruptions of the Old Faithful Geyser during part of August 1985. 80 81 84 74 93 80 108 62 81 51 71 50 54 85 54 60 50 79 74 82 57 89 85 75 86 92 77 54 59 58 80 54 58 65 53 43 57 80 81 81 75 90 79 76 78 89 80 73 66 49 77 73 57 58 52 60 61 81 87 92 60 60 88 91 83 84 82 62 53 50 86 83 68 50 60 69 48 81 80 88 77 65 76 87 87 74 81 71 50 62 56 82 78 48 49 71 73 79 87 93 (a) Go to the webpage www.public.iastate.edu/∼wrstephe/stat101.html. There is is a link for Old Faithful Data for Homework 2. Click on the right mouse button and select Save Link As. Save this file as geyser.txt on either the computer’s hard drive, or on a diskette. (b) Start the JMP program and select File → Open from the JMP menu. Enter the name of the file (geyser.txt), and change the Files of type: settings to Text Import Preview. Then click on Open and then Delimited. In the box that appears, click on Space in the End of Field Box. Put a check mark in the box near Table contains column headers. Click on Apply Settings. At this point, JMP gives you a preview of the column names and the first two rows of your data. If everything looks good, press OK. (c) We want to describe the distribution of this data. Select Analyze → Distribution from the JMP menu. Select the column Times and click the button Y, Columns. Then click on OK. (d) You should now have a histogram, boxplot, and statistics for this data set. We want to make a few changes to the information JMP has calculated. First, click on the red triangle next to Times and select Stem and Leaf. This should add a stem-and-leaf plot to your window. Now, click on the red triangle next to Times and select Histogram Options → Count Axis. This should add a count axis to the histogram in the window. Again, click on the red triangle next to Times and select Display Options → Horizontal Layout. (e) From the JMP Menu, select File → Print to print your output. Turn this in with your assignment. Using this output, answer the following questions on a separate piece of paper. i. What percentage of the times between eruptions are less than one hour? greater than an hour and a half? ii. Describe the shape of this distribution. Based on your answer, would you expect the mean to be equal to, less than, or greater than the median? Explain your answer. iii. Give the five number summary for these data. iv. Give the mean and standard deviation for these data. v. Did JMP split the stems in the stem plot? If yes, how did JMP split the stems? If no, do you think JMP should have split the stems? 2