Question 1118455
t0.975,df=29 is 2.045
standard error is s/sqrt(n)=200/sqrt(30)=36.51 or 37.
95% CI is mean +/- t0.975,df=29*s/sqrt(n)=2.045*37=mean +/- $75.67
($338.33, $489.67)

Assume a t=2
want half-interval to be $12
12=2*200/sqrt(n)
12*sqrt(n)=400
square both sides
144n=160,000
n=1111.1 or 1112
With this number, t can be approximated with z, and 95% interval is
1.96*200/sqrt(n)=12
392^2=144n
n=1067.1 or 1068