Question 1201568
<font color=black size=3>
Answer:  <font color=red size=4>423</font>



Explanation:


At 90% confidence, the z critical value is roughly z = 1.645
Use a table like this
<a href = "https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
to get that value. Look at the bottom row labeled "Z" and above the 90% confidence level.
A stats calculator can also compute this value.


We aren't told the phat value (sample proportion), so the best we can do is make a conservative estimate of phat = 0.5


We want the margin of error to be 4%, so E = 0.04


Summary input values:
z = 1.645 approximate
phat = 0.5
E = 0.04


We can now calculate the min sample size.
n = phat*(1-phat)*(z/E)^2
n = 0.5*(1-0.5)*(1.645/0.04)^2
n = 422.816406  approximately
n = 423  always round UP to the nearest whole number


That's how we arrive at the final answer of 423.
</font>