Question

1. In my class, 25 out of 32 students drive to school.

a) Find the critical value zα/2 for the 90% confidence level.

b) Find the margin of error E.

Answer 1

Solution :

Given that,

n = 25

x = 32

Point estimate = sample proportion = = x / n = 25/32=0.781

1 -   = 1-0.781 =0.219

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.781*0.219) / 32)

E = 0.1203

Margin of error = E 0.1203