Question

4. You want to do a study to see what the percentage of people is who think government is working well. Find the minimum sample size you should use to assure that your estimate of the true percentage will be within the required margin of error of 3%. The confidence level is 99%; from a prior study, p-hat is estimated as 0.34.

Answer 1

Solution :

Given that,

= 0.34

1 - = 1 - 0.34 = 0.66

margin of error = E = 3% = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.03)2 * 0.34 * 0.66

=1654.52

Sample size = 1655 rounded