Question

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 10001000 voters in the town and found that 29)% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 26&%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

We accept H₀

p-value = 0,1618

Explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test wants to test:

Null hypothesis H₀ p = p₀ or p = 26 %

Alternate hypothesis Hₐ p > p₀ or p > 26%

We assume CI 90 % then

α = 10 % α = 0,1 and z score for α = 0,1 is critical value

z = 2,32 ( note 2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s) = ( p -p₀ ) / √ p₀q₀/n

z(s) = ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

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

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618