Question

  According to a U.S. Census survey from 2010, 10% of American grandparents are raising their grandchildren. Find the sample size necessary to attain a margin of error that is at most 2% in estimating the population proportion of all American grandparents who are raising their grandchildren with a confidence level of 99%.

Question 10 options:

a.	1218
b.	798
c.	5410
d.	1493

Answer 1

Solution :

Given that,

= 10%=0.10

1 - = 1 - 0.10 = 0.9

margin of error = E = 2% = 0.02

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.576 / 0.02)2 * 0.10 * 0.9

=1493

Sample size = 1493