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3. An agronomist breed two rice varieties which are X variety that are long and aromatic grain and Y variety that are short and non-aromatic grain. The result of his first experiment resulted all rice offspring are long and aromatic. He wanted to continue his work using two hybrid rice from his experiment and wanted to confirm if he will yield the same ratio of Mendel's experiment from hybridization of two traits with 9:3:3:1 ratio. Months later, he harvested all the rice and segregated them according to their traits. He obtained the following results: Long and aromatic: 857 grains; Long and non-aromatic: 290 grains; short and aromatic: 320 grains; and, short and non-aromatic: 118 grains. a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 9:3:3:1 at 0.05 significance level? Why or why Not?

3. An agronomist breed two rice varieties which are X variety that are long and aromatic grain and Y variety that are short and non-aromatic grain. The result of his first experiment resulted all rice offspring are long and aromatic. He wanted to continue his work using two hybrid rice from his experiment and wanted to confirm if he will yield the same ratio of Mendel's experiment from hybridization of two traits with 9:3:3:1 ratio. Months later, he harvested all the rice and segregated them according to their traits. He obtained the following results: Long and aromatic: 857 grains; Long and non-aromatic: 290 grains; short and aromatic: 320 grains; and, short and non-aromatic: 118 grains. a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 9:3:3:1 at 0.05 significance level? Why or why Not?

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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ANSWER THE FOLLOWING QUESTIONS
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
Practice this Genetic Problem • Mendel's experiment on crossing pea flower with purple and white produced all purple as F1. He again bred two F1 purple. He observed 733 purple flower pea plants and 267 white flower pea plants. With our current knowledge of F2 phenotypic ratio of 3:1, does the outcome of Mendel's experiment coincides with the expected ratio? • You can use pen and paper and ready your calculator. • You can use the table format. Expected: Total number X Probability Ratio Purple : 1000 x (3/4) = 750 White : 1000 x (1/4) = 250 %3D %3D Phenotype Observed Expected Purple 733 750 White 267 250 I 10-E *TRY TO ANSWER IT FIRST! *ANSWERS are in White Color, to see Highlight the last column • There are two phenotypes so the df = 1, let us use the 0.05 significance level so the critical value is 3.84 • Is the computed Chi square value lesser than or greater than 3.84 • If you got greater value, try to practice it again • If you got lesser, you are correct! So we can say Mendel's experiment agree with the ratio of 3:1 QUESTION : 3. An agronomist breed two rice varieties which are X variety that are long and aromatic grain and Y variety that are short and non-aromatic grain. The result of his first experiment resulted all rice offspring are long and aromatic. He wanted to continue his work using two hybrid rice from his experiment and wanted to confirm if he will yield the same ratio of Mendel's experiment from hybridization of two traits with 9:3:3:1 ratio. Months later, he harvested all the rice and segregated them according to their traits. He obtained the following results: Long and aromatic: 857 grains; Long and non-aromatic: 290 grains; short and aromatic: 320 grains; and, short and non-aromatic: 118 grains. a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 9:3:3:1 at 0.05 significance level? Why or why Not?
Transcribed Image Text:Practice this Genetic Problem • Mendel's experiment on crossing pea flower with purple and white produced all purple as F1. He again bred two F1 purple. He observed 733 purple flower pea plants and 267 white flower pea plants. With our current knowledge of F2 phenotypic ratio of 3:1, does the outcome of Mendel's experiment coincides with the expected ratio? • You can use pen and paper and ready your calculator. • You can use the table format. Expected: Total number X Probability Ratio Purple : 1000 x (3/4) = 750 White : 1000 x (1/4) = 250 %3D %3D Phenotype Observed Expected Purple 733 750 White 267 250 I 10-E *TRY TO ANSWER IT FIRST! *ANSWERS are in White Color, to see Highlight the last column • There are two phenotypes so the df = 1, let us use the 0.05 significance level so the critical value is 3.84 • Is the computed Chi square value lesser than or greater than 3.84 • If you got greater value, try to practice it again • If you got lesser, you are correct! So we can say Mendel's experiment agree with the ratio of 3:1 QUESTION : 3. An agronomist breed two rice varieties which are X variety that are long and aromatic grain and Y variety that are short and non-aromatic grain. The result of his first experiment resulted all rice offspring are long and aromatic. He wanted to continue his work using two hybrid rice from his experiment and wanted to confirm if he will yield the same ratio of Mendel's experiment from hybridization of two traits with 9:3:3:1 ratio. Months later, he harvested all the rice and segregated them according to their traits. He obtained the following results: Long and aromatic: 857 grains; Long and non-aromatic: 290 grains; short and aromatic: 320 grains; and, short and non-aromatic: 118 grains. a) With the given problem, compute the chi square value. Show your solutions. b) Does the result follow the ratio of 9:3:3:1 at 0.05 significance level? Why or why Not?
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