Qrb_501_Week_5

Week 5 Assignment Seville & Somers Activity 18.1 1. Toss a coin 10 times and after each toss, record in the following table the result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence of heads and tails for the first five tosses: H T T T H. After the first toss, the proportion of heads so far is one out of one: 1/1 or 1. After the second toss, the proportion of heads so far is one out of two: 1/2. After the third toss, the proportion of heads is one out of three: 1/3. After the fourth toss, the proportion of heads is one out of four: 1/4. After the fifth toss, the proportion of heads is two out of five: 2/5. Toss # 1 2 3 4 5 6 7 8 9 10 H/T T H H H H T T H H T Prop of H so Far 0/1 1/2 2/3 3/4 4/5 4/6 4/7 5/8 6/9 6/10 2. On the following axes, plot the proportion of heads so far, for each toss from your table. What does the graph show' The plot shows that in the first few tosses the proportion can vary widely but overtime the proportion becomes normalized. Given enough time the plot will stabilize around 0.5 . 3. Now, you will use Excel to simulate 1000 independent tosses of a fair coin and plot on a graph the proportion of heads so far after each toss using the instructions that follow #3. 4. Write a paragraph explaining what your graph shows. Like I said in part 2, the graph begins with pretty wild and large differences in proportion but quickly begins to stabilize. Eventually this experiment ended with the proportion being around 52% of the coin tosses landing on heads. Again as the number increases, the likelihood of it eventually stabilizing at exactly 50% becomes more likely. 5. Put the cursor in any blank cell near your graph. Press Ctrl= to change the random numbers and your graph. Do this several times and describe how the graph changes. The graph usually has a different erratic pattern at the beginning, it varied from 0.3 to 0.7. Usually the proportion stabilized around toss 300 and eventually worked its way somewhere between 0.49 and 0.51. 6. Compute the overall proportion of hits by calculating the mean of the B column values. Also look at your data and identify the length of the longest streak of hits and the length of the longest streak of misses. Write a paragraph commenting on the proportion of hits and the “streaks.” I have included a chart to help in my explanation: Random Player (Player X) has a pretty good streak (for him) for the 1st 1/3rd of the data collected. He was averaging 55% success rate in his shots. Eventually then had a bad streak and dipped lower than 50% average around shot 53. That slump lasted till about shot 70. He then had a tiny upswing which brought his overall standing to exactly 50%. From the data I see only 2 real “streaks”. One is a downward trend from shot 48 to 56 (8 shots) and then an upward streak from 67 to 80(13 shots). My definition of a streak was 7 or more shots that trended in one direction. Toward the end there appears a downward spiral but it is broken up by a sucessful shot randomly in the data. 7. e. Find the overall proportion of hits, and identify the length of the longest streak of hits and the length of the longest streak of misses. Write a paragraph commenting on your proportion of hits and your “streaks.” The team, after 100 free throw attempts has a 76% success rate. The longest streak of hits was from shot #33 to shot #45. During these 12 shots the team percent increased by 0.8%. In this particular set of data there was no real downward streak. The only area that could remotely be considered this would be from shot #46 to shot #49 where they dropped a half a percentage point. Considering this happened over the course of 3 shots I would not consider this to be a streak. f. Describe how the “streaks” compare for the 50-percent and 75-percent scenarios. Comparing the 2 sets of data (50% and 75%) the streaks seems to be happening more in the 50% data set. With the 75% data set the streaks are more violent and short and on the 50% they are more gradual and long. This would eventually even out over the course of longer periods of study. Lind, Marchal & Wathern Ch2, Exercise 11 A and C The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting, Inc. during the first quarter of 2004. a) How many employees were studied: 50 employees were studied c) Construct a histogram Lind, Marchal & Wathern Ch3, Exercise 85 Refer to the CIA data, which reports demographic and economic information on 46 countries. a) Select the variable in Life Expectancy 1. Find the mean, median, and the standard deviation. i. Mean = 73.81 ii. Median = 76.10 iii. Standard Deviation = 6.90 2. Write a brief summary of the distribution of life expectancy. I took the data and created a histogram with Megastat. Based on this visual of the data, life expectancy is skewed to the left. There are 2 outliers that are on the left side of the graph and this can cause the mean to be pulled to the left. Because of this, I would say that the median gives a more accurate portrayal of the midpoint of this data. b) Select the variable GDP/cap. 1. Find the mean, median, and the standard deviation. i. Mean = 16.58 ii. Median = 17.45 iii. Standard Deviation = 9.27 2. Write a brief summary of the distribution GDP/cap. Again, I took the data and ran it through Megastat. Based on the graphical interpretation of the data, it appears to be bi-modal with peaks around 5 and 20. 21.7% of the countries are in the 5 to 10 range and 30.4% are in the 20 to 25 range. Less than half of the countries are lower, in between or higher than these to peaks but 52.1% lies in the bimodal peaks. Seville & Somers Activity 17.1 1 Only 1. Work with a partner to generate the following data: a. Toss 10 coins and record the number of heads you obtained. b. Repeat this 24 more times until you have a list of 25 numbers, each between 0 and 10. c. Retrieve the file “EA17.1 Coins and Presidents.xls” from the CD or website, and you will find the results of 35 tosses of 10 coins that someone else carried out. When you first retrieve the file, column B contains the number of times 0 heads was obtained in the 35 tosses of 10 coins, the number of times 1 head was obtained in the 35 tosses, and so on, up to the number of times 10 heads was obtained. Add your results to the list so you have a total of 60 in column B.   Number of Heads Frequency 0 0 1 1 2 2 3 5 4 9 5 18 6 13 7 8 8 3 9 1 10 0 d. Create a scatterplot of these data, using one of the versions of the scatterplot with the dots connected. Describe what your curve looks like, including where it is “centered” and what its “spread” is. The scatterplot is pretty much centered over 5. It gradually increases from 0 to 5 and it decreases from 5 to 10. The curve is spread pretty evenly and it is not skewed to either side. e. Change your graph to a bar graph. f. Print your bar graph, with appropriate titles on the axes, and by hand draw in a bell-shaped curve that “fits” this data. How does your handdrawn curve compare with the curve you described in part d of this question' The histogram with a line drawn (with the computer freehand drawing) ends up looking almost exactly like the scatterplot. Lind, Marchal & Wathern Ch17, Exercise 20 A and B A new machine has just been installed to cut and rough-shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each hour, measured the outside diameter, and recorded the results. The measurements (in millimeters) for the period 8:00 A.M. to 10:30 A.M. follow. Outside Diameter (millimeters) Time 1 2 3 4 5 8:00 87.1 87.3 87.9 87 87 8:30 86.9 88.5 87.6 87.5 87.4 9:00 87.5 88.4 86.9 87.6 88.2 9:30 86 88 87.2 87.6 87.1 10:00 87.1 87.1 87.1 87.1 87.1 10:30 88 86.2 87.4 87.3 87.8 a. Determine the control limits for the mean and the range. Control Limits for the Mean: Control Limits for the Range: Plot the control limits for the mean outside diameter and the range. Seville & Somers Activity Topic 17, exploration 2 2. a) Use a calculator or computer to compute the mean and standard deviation of the year 2000 revenue for the Pennsylvania companies in the first table. Mean = 631.25 Standard Deviation = 741.68 b) Use a calculator or computer to compute the mean and standard deviation of the year 2000 revenue for the Michigan companies in the second table. Mean = 210.17 Standard Deviation = 195.70 c) Explain what the values you calculated in parts a and b of this exploration tell you about the data sets. The Pennsylvania companies had a much larger mean with a much larger standard deviation. The Pennsylvania companies also had a much larger spread (1926.3) than the Michigan companies (728). d) How would the mean and standard deviations change if the largest data value in each set were removed' Pennsylvania: Mean = 435.71 Standard Deviation=533.78 Michigan: Mean=168.04 Standard Deviation=112.12 e) Find the mean and the standard deviation of the number of employees for the Pennsylvania companies in the first table. Mean=2973.6 Standard Deviation=3978.9 f) Find the mean and the standard deviation of the number of employees for the Michigan companies in the second table and compare to your results in part e of this exploration. Mean=782.9 Standard Deviation=960.9 The Pennsylvania companies have a higher mean and standard deviation than the Michigan companies. This also could explain the difference in the revenues from parts “a” and “b”.