Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Answer 1

We reject H₀ , we found enough evidence to support the claim

Explanation:

Sample size n = 1300

Sample proportion p = 45 % p = 0,45 and q = 0,55

Proportion of population p₀ = 42 % p₀ = 0,42

Hypothesis Test

Null Hypothesis H₀ p = 0,42

Alternative Hypothesis Hₐ P > 0,42

A one-tail test to the right is needed to evaluate the claim

Sample size big enough to consider binomial distribution can approximate to normal distribution

1300*p > 10 1300*q > 10

Significance level α = 0,02

z(c) fom z-table is z(c) = 2,05

To compute

z(s) = ( p - p₀ ) /√ (p*q)/n

z(s) = ( 0,45 - 0,42 ) /√ (0,45*0,55)1300

z(s) = 0,03 / 0,014

z(s) = 2,14

Comparing z(c) and z(s) z(s) > z(c) then z(s) s in the rejection region we must reject H₀ we found enough evidence to spport the claim