Answer:
The margin of error or the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.0406, which is 4.06 percentage points.
At the 85% confidence level, the margin of error would be smaller due to the lower value of Z.
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 .
The margin of error is:
90% confidence level
So , z is the value of Z that has a pvalue of , so .
In this problem, we have that:
So
The margin of error or the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.0406, which is 4.06 percentage points.
85% confidence level
So , z is the value of Z that has a pvalue of , so .
With the lower confidence level, z is lower, which means that the margin of error would be smaller.