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Answer:
The 95% confidence interval for the true proportion of Gastown residents living below the poverty line is (0.133, 0.2766).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence interval
, we have the following confidence interval of proportions.
In which
Z is the zscore that has a pvalue of .
For this problem, we have that:
He takes a simple random sample of 122 people living in Gastown and finds that 25 have an annual income that is below the poverty line. This means that and
We have , z is the value of Z that has a pvalue of
= 0.975, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the true proportion of Gastown residents living below the poverty line is (0.133, 0.2766).
Answer:
It isn't necessary but having a positive coefficient for makes things like completing the square and factoring easier.