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 Phenotype Observed Expected Purple 733 750 White 267 250 E 10-E 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 : 1. 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?

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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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
(0-E
E
Purple
733
750
White
267
250
E 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 Mendeľ's experiment
agree with the ratio of 3:1
QUESTION :
1. 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: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 (0-E E Purple 733 750 White 267 250 E 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 Mendeľ's experiment agree with the ratio of 3:1 QUESTION : 1. 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?
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
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