Question

A political study took a sample of 1600 voters in the town and found that 42% 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 39%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

P- value = 0.0069

Explanation:

Given that :

sample size n = 1600

The sample proportion
`\hat p` = 0.42

The population proportion p = 0.39

The null hypothesis and the alternative hypothesis can be expressed as:

`H_o : p =0. 39`

`H_1 : p >0.39`

The test statistics can be computed as follows:

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

`Z = \frac{0.42 - 0.39 }{\sqrt{(0.39(1-0.39))/(1600)}}`

`Z = \frac{0.03 }{\sqrt{(0.2379)/(1600)}}`

`Z = \frac{0.03 }{\sqrt{1.486875 * 10^(-4)}}`

`Z = (0.03 )/(0.0121937484)`

`Z = 2.4603`

Z
`\simeq` 2.46

Determine the P-value of the test statistic.

The P- value = P(Z >
`Z_o` )

P- value = 1 - P( Z ≤ 2.46)

Using the Excel Function ( = NORMSDIST (2.46))

P- value = 1 - 0.993053

P- value = 0.006947

P- value = 0.0069 to four decimal places