Question

In each​ case, find the approximate sample size required to construct a 90​% confidence interval for p that has sampling error SE=0.07. a. Assume that p is near 0.4. b. Assume that you have no prior knowledge about​ p, but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

a. The approximate sample size is _____

b. The approximate sample size is _____

Answer 1

a) Solution:

Given that:

E= 0.07

= 0.4

1 - = 1 - 0.4 = 0.6

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90= 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = ( Z/2 / E)2 * * (1 - )     

   = ( 1.645/ 0.07 )2 *0.4 *0.6

                   = 132.54

n = 133

b)

Solution:

Given that:

E= 0.07

= 0.5

1 - = 1 - 0.5 = 0.5

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90= 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = ( Z/2 / E)2 * * (1 - )     

   = ( 1.645/ 0.07 )2 *0.5 *0.5

                   = 138.06

n = 139