The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1100 voters in the town and found that 37% 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 34%. State the null and alternative hypotheses.

Null hypothesis:  

Alternative hypothesis:

Step-by-step explanation:

Data given and notation

n=1100 represent the random sample taken

estimated proportion of residents favored annexation

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be: