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

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p =0.80

H_a : p 0.80

n = 206

x = 154

= x / n = 154 / 206 =0.75

P₀ = 0.80

1 - P₀ = 1 - 0.80 = 0.20

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.75 - 0.80 / [(080*0.20) / 206]

= -1.88

Test statistic = z = -1.88

P(z < -1.88) = 0.0301

P-value = 2 * 0.0301 = 0.0602