Question

Let α = .05. A study out of Harvard wants to test the claim that the proportion of students who consider themselves Democrats and the proportion students who consider themselves Republicans are equal. Harvard takes a sample size of 1,003 and finds that 529 consider themselves Democrats. Using ρ0 = .5 do we have evidence to conclude that there is a significant difference between political affiliation among students? Make sure to write out the hypothesis, show all work, and state your conclusion. Which test did you use?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p 0.50

= x / n = 529/1003 = 0.527

P₀ = 0.50

1 - P₀ = 1-0 .50 =0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.527 - 0.50 / [0.50(1- 0.50 ) /1003 ]

= 1.737

P(z > 1.737) = 1 - P(z < 1.737 ) = 0.0824

P-value = 0. 0824

= 0.05

p = 0.0824 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population proportion p is different than p₀ at the α = 0.05 significance level.