Question

1. George Mendel conducted hybridization of peas. One experiment resulted in 580 peas with 26.2% having yellow pods. According to the theory, 25% of the peas should have yellow pods. Using a = 0.05, to test the claim that the proportion of peas with yellow pods is equal to 25%. (two tails)

   1. H0: p = ________

   2. H1: p ≠ ________

   3. z-score________

   4. P=_______

   5. Reject or fail to reject________

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

= 0.262

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.262 - 0.25 / [(0.25 * 0.75) / 580 ]

Test statistic = z = 0.67

P(z > 0.67) = 1 - P(z < 0.67) = 1 - 0.7486 = 0.2514

P-value = 2 * 0.2514 = 0.5028

= 0.05    

P-value >

Fail to reject the null hypothesis .