Question

Mendel observed in a sample of 580 peas that 152 were yellow peas. Mendel’s claim was that 25% of peas will be yellow. Use a 0.05 significance level. Find the P-value and state the conclusion.

Answer 1

Solution :

Given that ,

n = 580

x = 152

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

This is the two tailed test .

= x / n = 152 / 580 = 0.2621

P₀ = 25% = 0.25

1 - P₀ = 1 - 0.25 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2621 - 0.25 / [0.25 ( 1 - 0.25 ) / 580 ]

= 0.671

The test statistic = 0.671

P-value = 0.5021

= 0.05   

0.5021 > 0.05

P-value >

Fail to reject the null hypothesis .

Conclusion : - The null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than 25% at the α = 0.05 significance level.