Question

a genetic model suggests that 80% of plants grown from a cross between two given strains of seeds will be of the dwarf variety. after breeding 206 of these plants, 154 were observed to be of the dwarf variety. do these data strongly contradict the genetic model? find the p-value.

Answer 1

(H) We cannot conclude that the data contradict the genetic model since the p-value is greater or equal to 0.02

Solution:

Let p denotes the true proportion of plants grown from a cross between two given strains of seeds that will be of the dwarf variety.

$To test H_0:p = 0.8 against H_1:p \neq 0.8$

Here

$sample proprotion \hat{p} = \frac{152}{205} = 0.741463$

and sample size n = 205

The test statistic can be written as

$z = \frac{(\hat{p}-0.8)}{\sqrt{\frac{0.8*(1-0.8)}{n}}}$ which under H0 follows a standard normal distribution.

We reject H0 at a 2% level of significance if P-value < 0.02

Here

The value of the test statistic z_{obs} = -2.09529

P-value

$=P(|Z| < z_{obs}) = P(|Z| < -2.09529) = 2*P(Z < -2.09529) = 2*0.0180726 = 0.0361452$

Since P-value = 0.0361452 > 0.02, so we fail to reject H0 at a 2% level of significance.

Typical features of model organisms in addition to being well understood include rapid development to maturity ability to be easily manipulated short lifespan production of large numbers of offspring and retention of sequenced genomes. Genetic association analysis mode for investigating associations with dominant alleles. Comparison groups are homozygous wild-type genotypes and allele-positive.

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