Question

use the normal distribution and given sample results to complete the tests of the given hypothesis as soon as results come from a random sample and use 5% significance level

Test Ho : p = 0.3 vs Ha : p < 0.3 using the sample results p^ = 0.19 with n = 202

Answer 1

Solution :

The null and alternative hypothesis is

H₀ : p = 0.3

H_a : p < 0.3

= 0.19

1 - P₀ = 0.7

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.19 - 0.3 / [(0.3 * 0.7) / 202]

= -3.412

P(z < -3.412) = 0.0003

P-value = 0.0003

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the population proportion is leas than 0.3