Question

Name: ckhol hoor 1. Everyone knows that when you flip a coin, you have a 50 percent chance of heads and a 50 percent chance of tails. This means that out of 100 flips you should get 50 heads and 50 tails. However, if you actually flip a coin 100 times, a 50:50 ratio is only one among many possible outcomes. What if you get a ratio of 48 heads to 52 tails? How can we be certain that what we observe agrees with what we expect taking into account the role that chance plays Use the x (chi square) formula to determine if the observed ratios are due to chance tab caps lock shift 2. A large ear of corn has a total of 433 grains, including 271 Purple & starchy Your Tentative Hypothesis: This ear of corn was produced by a dihybrid cross (PpSs x PpSs) involving two 73 Purple &sweet 63 Yellow & starchy 26 Yellow & sweet pairs of heterozygous genes resulting in a theoretical (expected) ratio of 9:331 Objective: Test your hypothesis using chi square and probability values 3. A sample of mice (all from the same parents) shows 58 Black hair, black eyes 19 White hair, black eyes 16 Black hair, red eyes 7 White hair, red eyes. What is the expected genotypes of the parents? Objective: Perform a chi-square analysis to support your hypothesis

Answer 1

(1) χ² = ∑[(O – E)² / E]

	Experiment (100 flips)
	Heads	Tails
O (Observed)	48	52
E (Expected)	50	50
O – E	-2	2
(O – E)2	4	4
(O – E)2 / E	0.08	0.08
χ2	0.16

Degree of freedom = (n-1) = (2-1) = 1

χ² for DF=1 from Chi-square table for 95% confidence level is 3.84. This is critical χ²

Calculated χ² ≤ Critical χ²

Therefore, there is no statistical significance between the observed ratio (48:52) and the expected ratio of (50:50).

(2) χ² = ∑[(O – E)² / E]

	Experiment (Dihybrid cross)
	Purple & Starchy	Purple & Sweet	Yellow & Starchy	Yellow & Sweet
O (Observed)	271	73	63	26
E (Expected)	(9/16)(433) = 243.5	(3/16)(433) = 81.2	(3/16)(433) = 81.2	(1/16)(433) = 27.1
O – E	27.5	-8.2	-18.2	-1.1
(O – E)2	756.25	67.24	331.24	1.21
(O – E)2 / E	3.1	0.82	4.08	0.045
χ2	8.045

Degree of freedom = (n-1) = (4-1) = 3

χ² for DF=3 from Chi-square table for 95% confidence level is 7.81. This is critical χ²

Calculated χ² ≥ Critical χ²

Therefore, there is a statistical significance between the observed ratio and the expected ratio. The cross does not result in a ratio of 9:3:3:1.

(3) Hypothesis: The genotype of the parents is Black hair and Black eyes (BbEe x BbEe). This follows the Mendel dihybrid ratio of 9:3:3:1.

	Experiment (Dihybrid cross)
	Black hair & Black eyes	Black hair & Red eyes	White hair & Black eyes	White hair & Red eyes
O (Observed)	58	16	19	7
E (Expected)	(9/16)(100) = 56.25	(3/16)(100) = 18.75	(3/16)(100) = 18.75	(1/16)(100) = 6.25
O – E	1.75	-2.75	0.25	0.75
(O – E)2	3.06	7.56	0.06	0.56
(O – E)2 / E	0.054	0.4	0.003	0.09
χ2	0.547

Degree of freedom = (n-1) = (4-1) = 3

χ² for DF=3 from Chi-square table for 95% confidence level is 7.81. This is critical χ²

Calculated χ² ≥ Critical χ²

Therefore, there is a no statistical significance between the observed ratio and the expected ratio.