12 value 142 points Construct a 90 percent confidence interv

12.

value:
1.42 points

Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back.(Round your answers to 4 decimal places.)

Of 43 bank customers depositing a check, 23 received some cash back.

(a)p=23/43 = 0.5348837

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.5348837 -1.645*sqrt(0.5348837*(1-0.5348837)/43) =0.4098

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.5348837 +1.645*sqrt(0.5348837*(1-0.5348837)/43) =0.6600

---------------------------------------------------------------------------------------------------------------------------

(b) Yes