Question

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1100 voters in the town and found that 54% 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 50%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

The p-value is
`p-value = 0.0039854`

Explanation:

From the question we are told that

The sample size is n = 1100

The population proportion is p = 0.50

The sample proportion is
`\^ p = 0.54`

The null hypothesis is
`H_o : p = 0.50`

The alternative hypothesis is
`H_a : p > 0.50`

Generally the test statistics is mathematically represented as

`z = \frac{\^ p - p }{ \sqrt{( p(1 - p))/(n) } }`

=>
`z = \frac{ 0.54 - 0.54 }{ \sqrt{( 0.50 (1 - 0.50))/(1100) } }`

=>
`z = 2.6533`

Generally from the z-table the probability of 2.6533 for a right tailed test is

`p-value = 0.0039854`