Answer:
a) z = 2.327
b) The margin of error is of 0.065.
c) The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, 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:
a) 98% confidence level
So , z is the value of Z that has a pvalue of
, so
is the critical value.
b)
The margin of error is:
So, applying to this question:
The margin of error is of 0.065.
c) Find confidence interval for the problem.
The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).