Question

The mayor claims that the African Americans account for 27% of all city employees. A civil rights group disputes the claim and argues that the city discriminates against African Americans. A random sample of 110 city employees has 25 African Americans. Test the mayors claim at a .01 level of significance.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.27

H_a : p 0.27

n = 110

x = 25

= x / n = 25 / 110 = 0.2273

P₀ = 0.27

1 - P₀ = 1 - 0.27 = 0.73

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2273 - 0.27 / [(0.27 * 0.73) / 110]

= -1.009

Test statistic = -1.009

P(z < -1.009) = 0.1565

P-value = 2 * 0.1565 = 0.313

= 0.01

P-value >

Fail to reject the null hypothesis .