Question

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (For each answer, enter a number. Round your answers up the nearest whole number.)

(a)

a preliminary estimate for p is 0.23

(b)

there is no preliminary estimate for p

Answer 1

Solution :-

Given that,

a) = 0.23

1 - = 1-0.23 = 0.77

margin of error = E = 0.1

Z_/2 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96/0.1)² * 0.23*0.77

= 68

sample size = n = 68

b)

= 0.50

1 - = 1-0.50 = 0.50

margin of error = E = 0.1

Z_/2 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96/0.1)² * 0.50*0.50

  = 96

sample size = n = 96