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
, and a confidence level of  , we have the following confidence interval of proportions.
, 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
, z is the value of Z that has a pvalue of  , so
, so  is the critical value.
 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).