Question

estimate= 0.46

SE= 0.023

X=210

n=461

critical value= 1.96

95% confidence intravel

what is the:

estimate of error (plus and minus)

lower limit

upper limit

Answer 1

Solution :

Given that,

n = 461

x = 210

= x / n = 210/461 =0.46  

1 - = 1 - 0.46 = 0.54

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 (critical value)

SE=(( * (1 - )) / n) =((0.46 * (0.54)) / 461) =0.023

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96* ((0.46 * (0.54)) / 461) = 0.045

A 95 % confidence interval for proportion p is ,

- E < P < + E

0.46 - 0.045 < p < 0.46 + 0.045

0.415 < p < 0.505

LOWER LIMIT = 0.415

UPPER LIMIT = 0.505