In snapdragons, variation in flower color is determined by a single gene. RR ind
ID: 3131527 • Letter: I
Question
In snapdragons, variation in flower color is determined by a single gene. RR individuals are red, Rr (heterozygous) individuals are pink, and rr individuals are white. In a cross between heterozygous individuals, the expected ratio of red-flowered:pink-flowered:white-flowered offspring is 1:2:1. a) The results of such a cross were 10 red-, 21 pink-, and 9 white-flowered offspring. Do these results differ significantly (at a 5% level) from the expected frequencies? b) In another, larger experiment, you count 100 times as many flowers as in the experiment in part (a) and get 1000 red, 2100 pink, and 900 white. Do these results differ significantly from the expected 1:2:1 ratio? c) Do the proportions observed in the two experiments [i.e., in parts (a) and (b) differ? Did the results of the two hypotheses tests differ? Why or why not/
Explanation / Answer
a)
Doing an observed/expected value table,
O E (O - E)^2/E
10 10 0
21 20 0.05
9 10 0.1
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 0.15
As df = a - 1,
a = 3
df = a - 1 = 2
Then, the critical chi^2 value is
significance level = 0.05
chi^2(crit) = 5.991464547
As chi^2 < 5.99, we FAIL TO REJECT HO.
Hence, they do not significantly differ from the expected frequencies. [ANSWER]
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b)
Doing an observed/expected value table,
O E (O - E)^2/E
1000 1000 0
2100 2000 5
900 1000 10
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 15
As df = a - 1,
a = 3
df = a - 1 = 2
Then, the critical chi^2 value is
significance level = 0.05
chi^2(crit) = 5.991464547
As chi^2 > 5.99, we reject Ho.
Hence, they significantly differ from the expected frequencies. [ANSWER]
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c)
The sample proportions do not differ, but part b) significantly differed from the hypothesized distribution due to its large sample size.
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