The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1700 voters in the town and found that 66% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 63%.
A) Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.

Step-by-step explanation:

Data given and notation

n=1700 represent the random sample taken

estimated proportion of voters that favored construction

is the value that we want to test

represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

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 percentage of residents who favor construction is more than 63%.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statisitc, 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 significance level provided . The next step would be calculate the p value for this test.  

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

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.

step-by-step explanation:

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