1. Genotypes AA, Aa and aa occur with probabilities [02/4,0(1 – 0/2), (1 – 0/2)²]. A multinomial sample of size n has frequencies (n1, N2, N3) of these three genotypes. (a) Write down and simplify the log-likelihood. (b) Show that the maximum likelihood estimate of 0 is Ô = the asymptotic standard error of ê. 2n1 +n2 == and find N1 N2 N3 (c) If n₁ = 12, n₂ = 20 and n3 = 18, conduct a score test of Ho: 0 = 1 against : H₁ 01 (reporting the test statistic and p-value), and find a score test based 95% confidence interval for 0.
1. Genotypes AA, Aa and aa occur with probabilities [02/4,0(1 – 0/2), (1 – 0/2)²]. A multinomial sample of size n has frequencies (n1, N2, N3) of these three genotypes. (a) Write down and simplify the log-likelihood. (b) Show that the maximum likelihood estimate of 0 is Ô = the asymptotic standard error of ê. 2n1 +n2 == and find N1 N2 N3 (c) If n₁ = 12, n₂ = 20 and n3 = 18, conduct a score test of Ho: 0 = 1 against : H₁ 01 (reporting the test statistic and p-value), and find a score test based 95% confidence interval for 0.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...
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![1. Genotypes AA, Aa and aa occur with probabilities [02/4,0(1 – 0/2), (1 – 0/2)²]. A
multinomial sample of size n has frequencies (n1, N2, N3) of these three genotypes.
(a) Write down and simplify the log-likelihood.
(b) Show that the maximum likelihood estimate of 0 is Ô =
the asymptotic standard error of ê.
2n1 +n2
==
and find
N1 N2 N3
(c) If n₁ = 12, n₂ = 20 and n3 = 18, conduct a score test of Ho: 0 = 1 against
:
H₁ 01 (reporting the test statistic and p-value), and find a score test based
95% confidence interval for 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F008f8cce-1e45-43a4-8b17-46721d7357f5%2F77eb4b6b-f155-415f-b046-f2ca82ecc0ed%2F64bbtth_processed.png&w=3840&q=75)
Transcribed Image Text:1. Genotypes AA, Aa and aa occur with probabilities [02/4,0(1 – 0/2), (1 – 0/2)²]. A
multinomial sample of size n has frequencies (n1, N2, N3) of these three genotypes.
(a) Write down and simplify the log-likelihood.
(b) Show that the maximum likelihood estimate of 0 is Ô =
the asymptotic standard error of ê.
2n1 +n2
==
and find
N1 N2 N3
(c) If n₁ = 12, n₂ = 20 and n3 = 18, conduct a score test of Ho: 0 = 1 against
:
H₁ 01 (reporting the test statistic and p-value), and find a score test based
95% confidence interval for 0.
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