Question

#6: (a) 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 204 of these plants, 154 were observed to be of the dwarf variety. Do these data strongly contradict the genetic model? Find the p-value (b) At the 5% significance level, what is the conclusion of the above hypothesis test? #6(a) p-value (correct to 4 decimals) (A) We cannot conclude that the data contradict the genetic model since the p-value is less than .10 (B) We cannot conclude that the data contradict the genetic model since the p-value is greater or equal to .10 (C) We conclude that the data contradict the genetic model since the p-value is less than 10 (D) We conclude that the data contradict the genetic model since the p-value is greater than or equal to 0.05 (E) We cannot conclude that the data contradict the genetic model since the p-value is less than 0.05 (F) We cannot conclude that the data contradict the genetic model since the p-value is greater or equal to 0.05 (G) We conclude that the data contradict the genetic model since the p-value is greater than or equal to .10 (H) We conclude that the data contradict the genetic model since the p-value is less than 0.05 m #6(b) conclusion Select

Answer 1

Let p denotes the true proportion of plants grown to be of the dwarf variety.

To test
Ho p=0.80
against
Hp0.80 1

Here

sample proportion

154 0.754902 204

and sample size n = 204

The test statistic can be written as

which under H₀ follows a standard normal distribution.

p 0.8 0.8+ (1-0.8) 2 n

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

Zabs=-1.61032

P-value

P(|Z| = 2 P(Z< -1.61032) P(Z 1.61032) Zobs 2 0.0536638 0.107328 _

Conclusion : B) We cannot conclude that the data contradict the generic model since p-value is greater than or equal to 0.10