Question

The mayor of a town has proposed a plan for the annexation of an adjoining bridge. A political study took a sample of 900 voters in the town and found that 46% 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 over 43%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if p-value < 0.05

Now,

The value of the test statistic =

and p-value =

Since p-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that the percentage of residents who favor annexation is over 43%.