Question

1) A survey states that 280 out of 800 people smoke on a regular basis. Determine the required sample size if you want to be 90% confident that the sample proportion is within 3% of the population proportion.

2) Determine the required sample size if you want to be 99% confident that the sample proportion is within 2% of the population proportion if no preliminary estimate of the true population is available.

Answer 1

Solution :

Given that,

= x/n =280/800=0.35

1 - = 1 - 0.35= 0.65

margin of error = E = 3% = 0.03

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

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

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

= (1.645 / 0.03)2 * 0.35 * 0.65

=684.02

Sample size = 684

b

Solution :

Given that,

= 0.5

1 - =0.5

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 = 2.576 ( Using z table )

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

= (2.576 / 0.02)2 * 0.5 * 0.5

=4147.36

Sample size =4147 rounded