Question

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1300 voters in the town and found that 38% 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 over 35%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

Answer 1

We reject H₀, we have enough evidence to support the claim that the porcentage of residents who favor construction is over 35%

Explanation:

Sample size n = 1300

Sample proportion p = 38 % = 0,38 then q = 62% q = 0,62

The size of the sample is enough to consider the binomial distribution can approximate to normal distribution

p*n = 1300*0,38 q*n = 1300*0,62

p*n > 10 q*n> 10

Population proportion 35% p₀ = 35 % p₀ = 0,35

Hypothesis Test :

Null Hypothesis H₀ p = p₀

Alternative Hypothesis Ha p > p₀

The hypothesis test is a one-tail test to the right

Significance Level α = 0,05 we go to z-table and find z(c)

z(c) = 1,64

To calculate z(s)

z(s) = ( p - p₀ ) / √ p*q/ n

z(s) = 0,38 - 0,35 / √ ( 0,38 * 0,62) / 1300

z(s) = 0,03 / 0,013

z(s) = 2,307

Comparing z(c) and z(s)

z(s) > z(c) 2,307 > 1,64

z(s) is in the rejection region for H₀, we must reject H₀

We have enough evidence to support the claim