) When crossing a pure-breeding strain of tabby cats with a pure-breeding strain
ID: 272658 • Letter: #
Question
) When crossing a pure-breeding strain of tabby cats with a pure-breeding strain of black cats, all the offspring have a tabby coat. The tabby pattern is a grey-yellow background with black stripes, similar to those seen on tigers. Crossing the tabby offspring to each other gives a 3:1 ratio of tabby (T) to black (t) coat. Short hair (S) is dominant to long hair (s). The two characteristics of hair coloring and hair length are inherited independently of each other. One particular pair of dihybrid short-haired tabby cats produced twenty- two litters over a period of ten years (spay or neuter your cat!). Among these were 13 long-haired black kittens, 96 short-haired tabbies, 28 long-haired tabbies and 32 short- haired black kittens. 2) Perform another Chi square test on the same data trom problem # 1, testing instead the null hypothesis that the phenotypic ratio of the offspring is 3 short tabby: 1 short black :3 long tabby : 1 long black JTSS 3:Explanation / Answer
1. The answer is
Null hypothesis: The obseved values are not deviating from the expected values.
Test-staic: Chisquare test
Category
short tabbies
long tabbies
short tabbies
long black
Total
Observed values (O)
96
28
32
13
169
Exptected Ratio (ER)
9
3
3
1
16
Exprected Values (E)
95.0625
31.6875
31.6875
10.5625
Deviation (O-E)
0.9375
-3.6875
0.3125
2.4375
D^2
0.878906
13.59766
0.097656
5.941406
D^2/E
0.009246
0.429117
0.003082
0.5625
1.003945
X^2
1.003945
Degrees of freedom
4
-
1
3
Inference: The calculated chisquare value i.e. 1.00 is less than the table value i.e. 7.82 at 3 DF and 0.05 probability, hence the null hypothesis is accepted.
2.
Null hypothesis: The obseved values are not deviating from the expected values.
Test-staic: Chisquare test
Category
short tabbies
long tabbies
short tabbies
long black
Total
Observed values (O)
96
28
32
13
169
Exptected Ratio (ER)
3
3
1
1
8
Exprected Values (E)
63.375
63.375
21.125
21.125
Deviation (O-E)
32.625
-35.375
10.875
-8.125
D^2
1064.391
1251.391
118.2656
66.01563
D^2/E
16.79512
19.74581
5.598373
3.125
45.2643
X^2
45.2643
Degrees of freedom
4
-
1
3
Inference: The calculated chisquare value i.e. 45.26 is greater than the table value i.e. 7.82 at 3 DF and 0.05 probability, hence the null hypothesis is rejected.
Category
short tabbies
long tabbies
short tabbies
long black
Total
Observed values (O)
96
28
32
13
169
Exptected Ratio (ER)
9
3
3
1
16
Exprected Values (E)
95.0625
31.6875
31.6875
10.5625
Deviation (O-E)
0.9375
-3.6875
0.3125
2.4375
D^2
0.878906
13.59766
0.097656
5.941406
D^2/E
0.009246
0.429117
0.003082
0.5625
1.003945
X^2
1.003945
Degrees of freedom
4
-
1
3
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