Question

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.

Answer 1

Answer:

Null hypothesis:$p \leq 0.34$  

Alternative hypothesis:$p > 0.34$

$z=\frac{0.37 -0.34}{\sqrt{\frac{0.34(1-0.34)}{1100}}}=2.100$  

$p_v =P(z>2.100)=0.0179$  

Step-by-step explanation:

Data given and notation

n=1100 represent the random sample taken

$\hat p=0.37$ estimated proportion of residents favored annexation

$p_o=0.34$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of residents favored annexation is higher than 0.34 or 34%, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.34$  

Alternative hypothesis:$p > 0.34$  

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

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

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

Calculate the statistic  

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

$z=\frac{0.37 -0.34}{\sqrt{\frac{0.34(1-0.34)}{1100}}}=2.100$  

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:  

$p_v =P(z>2.100)=0.0179$