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Answer:
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.