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e: Coin FLIP an have a two probable outcomes, which are heads and tai say that when we flip a coin, there is a 50% chance for a he for tail as a result, thus, there will 50:50 or 1:1 ratio. tample, I flipped a coin 100 times. I got a result of 54 he tails. We already know that there is 50:50 or 1:1 ratio outcome. We can say that the expected outcome should s and 50 tails. hi Square Statistic//Test, can answer the question: esult (54 heads and 46 tails) is equal to the expected ratio esult (54 heads and 46 tails) deviated to the expected ratic fine first which is Observed and Exper ply substitute it in the formula given. (54-50), (46-50)? 50 50 You can also use tables like this: (43. (-43 Observed Expected

e: Coin FLIP an have a two probable outcomes, which are heads and tai say that when we flip a coin, there is a 50% chance for a he for tail as a result, thus, there will 50:50 or 1:1 ratio. tample, I flipped a coin 100 times. I got a result of 54 he tails. We already know that there is 50:50 or 1:1 ratio outcome. We can say that the expected outcome should s and 50 tails. hi Square Statistic//Test, can answer the question: esult (54 heads and 46 tails) is equal to the expected ratio esult (54 heads and 46 tails) deviated to the expected ratic fine first which is Observed and Exper ply substitute it in the formula given. (54-50), (46-50)? 50 50 You can also use tables like this: (43. (-43 Observed Expected

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Chi Square analysis
Example: Coin FLIP •A coin can have a two probable outcomes, which are heads and tails. • We can say that when we flip a coin, there is a 50% chance for a head and 50% for tail as a result, thus, there will 50:50 or 1:1 ratio. • As an example, I flipped a coin 100 times. I got a result of 54 heads and 46 tails. We already know that there is 50:50 or 1:1 ratio as possible outcome. We can say that the expected outcome should be 50 heads and 50 tails. • So the Chi Square Statistic/Test, can answer the question: Does my result (54 heads and 46 tails) is equal to the expected ratio? Does my result (54 heads and 46 tails) deviated to the expected ratio? Let us define first which is Observed and Expected, then, simply substitute it in the formula given. Σ 0 -EY - (54-50)°, (46-50)² 50 E 50 You can also use tables like this: (4 (-4) Observed Expected (0- EF 50 50 16 16 Heads 54 50 0.32 %3D 50 50 Tails 46 50 0.32 0.32 + 0.32 = 0.64 %3D I 10-E 0.64 Student: Sir, Is that all? • Not Yet, We just computed the Chi Square (x²) value for that example Critical values for x test • We should also know the dF or degrees of freedom *dF = n-1 ; where number of classes or categories 1 2 4.605 5.99 9.21 10.60 3 6.251 7.82 11.35 12.94 I 0.1 0.05 0.01 0.005 1 2.706 3.84 6.64 7.88 • We should compare it with the Critical Values of the x? Distribution (Table) 4 7.779 9.49 13.28 14.86 5 9.236 11.07 15.09 16.75 6 10.65 12.59 16.81 18.55 12.02 14.07 18.48 20.28 • Commonly used significance level is 0.05 or 5% 8 13.36 15.51 20.09 21.96 9 14.68 16.92 21.67 23.59 10 15.99 18.31 23.21 25.19 • From the example, there are only two outcomes (head or tail) so we substitute 2 for n, then we can compute for dF dF = n-1 ; dF = 2-1; dF = 1 • From the table, the critical value for dF=1 at 0.05 significance level is 3.84 • The calculated x² value is 0.64. Comparing it with 3.84, it is less than. 0.64 < 3.84, so the null hypothesis (1:1 ratio/ O=E) is accepted. • We can now say that the result of flip coin with 54 Heads and 46 Tails conform with the 1:1 ratio
Transcribed Image Text:Example: Coin FLIP •A coin can have a two probable outcomes, which are heads and tails. • We can say that when we flip a coin, there is a 50% chance for a head and 50% for tail as a result, thus, there will 50:50 or 1:1 ratio. • As an example, I flipped a coin 100 times. I got a result of 54 heads and 46 tails. We already know that there is 50:50 or 1:1 ratio as possible outcome. We can say that the expected outcome should be 50 heads and 50 tails. • So the Chi Square Statistic/Test, can answer the question: Does my result (54 heads and 46 tails) is equal to the expected ratio? Does my result (54 heads and 46 tails) deviated to the expected ratio? Let us define first which is Observed and Expected, then, simply substitute it in the formula given. Σ 0 -EY - (54-50)°, (46-50)² 50 E 50 You can also use tables like this: (4 (-4) Observed Expected (0- EF 50 50 16 16 Heads 54 50 0.32 %3D 50 50 Tails 46 50 0.32 0.32 + 0.32 = 0.64 %3D I 10-E 0.64 Student: Sir, Is that all? • Not Yet, We just computed the Chi Square (x²) value for that example Critical values for x test • We should also know the dF or degrees of freedom *dF = n-1 ; where number of classes or categories 1 2 4.605 5.99 9.21 10.60 3 6.251 7.82 11.35 12.94 I 0.1 0.05 0.01 0.005 1 2.706 3.84 6.64 7.88 • We should compare it with the Critical Values of the x? Distribution (Table) 4 7.779 9.49 13.28 14.86 5 9.236 11.07 15.09 16.75 6 10.65 12.59 16.81 18.55 12.02 14.07 18.48 20.28 • Commonly used significance level is 0.05 or 5% 8 13.36 15.51 20.09 21.96 9 14.68 16.92 21.67 23.59 10 15.99 18.31 23.21 25.19 • From the example, there are only two outcomes (head or tail) so we substitute 2 for n, then we can compute for dF dF = n-1 ; dF = 2-1; dF = 1 • From the table, the critical value for dF=1 at 0.05 significance level is 3.84 • The calculated x² value is 0.64. Comparing it with 3.84, it is less than. 0.64 < 3.84, so the null hypothesis (1:1 ratio/ O=E) is accepted. • We can now say that the result of flip coin with 54 Heads and 46 Tails conform with the 1:1 ratio
2. A researcher transferred two hybrid Red color fishes, from a pure line Red color fish as dominant and pure line White color fish as recessive, in a large aquarium for breeding purposes. After few months, fingerlings were seen inside the aquarium, however, two colors of the fishes were observed. The researcher counted the fingerlings and obtained 133 red color fishes and 38 white color fishes. The researcher did not know if the result followed the Mendelian genetic ratio of 3:1? a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 3:1 at 0.05 significance level? Why or why not?
Transcribed Image Text:2. A researcher transferred two hybrid Red color fishes, from a pure line Red color fish as dominant and pure line White color fish as recessive, in a large aquarium for breeding purposes. After few months, fingerlings were seen inside the aquarium, however, two colors of the fishes were observed. The researcher counted the fingerlings and obtained 133 red color fishes and 38 white color fishes. The researcher did not know if the result followed the Mendelian genetic ratio of 3:1? a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 3:1 at 0.05 significance level? Why or why not?
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