Gregor Mendel has been called the \"father of genetics,\" having formulated laws
ID: 3150870 • Letter: G
Question
Gregor Mendel has been called the "father of genetics," having formulated laws of inheritance even before the function of DNA was discovered. In one famous experiment with peas, he crossed pure breeds of plants producing smooth peas and plants producing wrinkled peas. The first generation peas were all smooth. In the second generation (F2), he obtained 5497 smooth peas and 1836 wrinkled peas. Use these data to try to refute Mendel's claim of 76% dominant trait (in this case "smooth") occurrence in F2. (a) State the hypotheses: H0: p = .76 Correct: Your answer is correct. and Ha: p .76 (b) Calculate the test statistic: (Use 2 decimal places) (c) Calculate the p-value: (Use 4 decimal places) (d) What should we decide when the significance level is .05? Reject the null hypothesis; Mendel's theory is refuted by the data. Reject the null hypothesis; Mendel's theory is not refuted by the data. Fail to reject the null hypothesis; Mendel's theory is refuted by the data. Fail to reject the null hypothesis; Mendel's theory is not refuted by the data.
Explanation / Answer
Set Up Hypothesis
Null, H0:P=0.76
Alternate, H1: P!=0.76
Test Statistic
No. Of Success chances Observed (x)=5497
Number of objects in a sample provided(n)=7333
No. Of Success Rate ( P )= x/n = 0.7496
Success Probability ( Po )=0.76
Failure Probability ( Qo) = 0.24
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.74962-0.76/(Sqrt(0.1824)/7333)
Zo =-2.0803
| Zo | =2.0803
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.08 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -2.08026 ) = 0.0375
Hence Value of P0.05 > 0.0375,Here we Reject Ho
[ANSWER]
a.
H0:P=0.76, H1: P!=0.76
b.
Zo =-2.08
c.
Ha : ( P != -2.08026 ) = 0.0375
d.
Mendel's theory is refuted by the data
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