Question

he mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 16001600 voters in the town and found that 344% 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 311%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

2.60

Explanation:

Given that:

n = 1600

`\hat p = 0.34`

`P_o = 0.31`

The test statistics can be computed as:

`Z = \frac{\hat p - P_o}{\sqrt{ \frac{P_o* (1-P_o) } {n} }}`

`Z = \frac{0.34-0.31}{\sqrt{ \frac{0.31 * (1-0.31) } {1600} }}`

`Z = \frac{0.03}{\sqrt{ \frac{0.31 * (0.69) } {1600} }}`

`Z = \frac{0.03}{\sqrt{ \frac{0.2139} {1600} }}`

`Z = 2.60`