MINITAB 5 MICHAEL CUAUTLA

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University Of Connecticut *

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1000

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Statistics

Date

Feb 20, 2024

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pdf

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Uploaded by KidIce12726

Assignment 5 Name: Michael Cuautla Section Number: 028D Date: Wed Oct 25, 2023 Please answer all ques,ons using the appropriate version of the dataset as assigned by your TA. Each graph must be labeled with a ,tle, axis labels, and a footnote with your name and sec,on number. Begin with a clear worksheet. 1. In this problem, you will compare the theore,cal probabili,es to experimental probabili,es that you obtain using rela,ve frequencies from a random sample. You will use a coin ﬂipping example since everyone is familiar with it. All of us know that the probability of a head is .5 when a fair coin is ﬂipped. If you ﬂip a coin 10 ,mes, then this is a binomial experiment with n=10 and p=.5. a. First, create the theore,cal probability distribu,on table, as explained above in parts A and B of the lesson. (Please note: In this example, n=10 and p=.5) Print this theore,cal distribu,on in the Session Window (by leaving the Op4onal Storage field blank) so that you will have an output display of the theore,cal probabili,es for comparison purposes. In the display, no,ce that the theore,cal probability of observing 3 heads in the 10 ﬂips is 0.1172. Your experimental probability of 3 heads in 10 ﬂips should be close to this. b. Next, you could run an experiment in which 200 people ﬂip a coin 10 ,mes each and record the number of heads they observe. You could then create a frequency table by coun,ng up the number of people who ﬂipped 0 Heads, 1 Head, 2 Heads, etc. If you then calculated the rela,ve frequencies, you could compare them to the theore,cal probabili,es printed in your Session Window. Since finding 200 people who would be willing to ﬂip a coin 10 ,mes would be ,me consuming, you will let the computer simulate the experiment by genera,ng 200 random samples of size 10, and storing the number of successes for each sample in one column. First, generate the 200 random samples of size 10. Click on: CALC → RANDOM DATA → BINOMIAL Fill in the screen as follows: Generate 200 Rows of Data Store in column(s) : C3 Number of Trials : 10 Probability of Success : .5 Look at C3. Each of the 200 cells should contain a number between 0 and 10. This represents the number of Heads observed by each person. (Each cell represents a person.) Next, have MINITAB create the frequency table for you.

Click on: STAT → TABLES → TALLY INDIVIDUAL VARIABLES Fill in the screen as follows: Variables : C3 Select: COUNTS (an X should appear in the box) Select: PERCENTS (an X should appear in the box) A frequency table will appear in the Session Window. Look carefully at the table. Under the heading C3, you would like to see the numbers from 0 to 10. Because your data is random, it is possible that nobody observed 0 Heads or 10 Heads. In this case, the 0 and 10 will not appear under C3. Under the heading Count, you will see the frequencies. These represent the number of people (out of the 200 people) who tossed that number of Heads. Under the heading Percent, you will see the rela,ve frequencies, as percentages. Compare these rela,ve frequencies to the theore,cal probabili,es that you produced earlier in the Session Window. Since this is random data, each student’s frequency table will be a li‘le different. In the chart below, fill in the theore,cal and experimental probabili,es using the computer output. Be sure to convert the rela,ve frequency percentages to probabili,es by moving the decimal point two places to the leb so that you can make a direct comparison with the theore,cal probabili,es. ( Round all probabili4es to 3 decimal places.) How close are the experimental probabili,es to the theore,cal probabili,es? Write a brief comparison of the theore,cal and experimental probabili,es. For which X values are the probabili,es very close? Where is the biggest difference? How could you change the experiment to improve these es,mates? Theore4cal and experimental probabili4es closely matched, with an exact match in one instance. The probabili4es were similar across all X values, except when X equaled 0 heads and 10 heads, where a 4ny 0.0009% difference emerged. The most significant varia4on was evident when considering 5 heads, with a 4% disparity. To enhance the experiment's reliability, one could consider conduc4ng mul4ple trials or involving a different person in the experimenta4on process. X T h e o r e , c a l Probability Experimental Probability Difference 0 0.0009 0 0.0009 1 0.009 0.005 0.004 2 0.43 0.04 0.003 3 0.117 0.1 0.017 4 0.2 0.2 0 5 0.24 0.28 -0.04 6 0.205 0.22 -0.007 7 0.11 0.95 0.006 8 0.04 0.5 -0.01 9 0.009 0.1 -0.01 10 0.0009 0 0.0009

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