2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor the construction of the nuclear plant at 5% significance level

So if we compare the p value and using any significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.  

Step-by-step explanation:

Data given and notation  

represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

represent the number of people suburban residents are in favor

sample 1 selected

sample 2 selected

represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We need to apply a z test to compare proportions, and the statistic is given by:  

  (1)

Where

Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

Statistical decision

The significance level provided is ,and we can calculate the p value for this test.  

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

So if we compare the p value and using any significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.