Question

1. Researchers designing a new study require a 99% probability that a sample proportion is within 0.5% of the population proportion. How large a sample size do they need? (No prior information is known about the sample proportion.)

   a. 7. b. 664. c. 66358. d. 16589

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =0.5% = 0.005

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 / 0.005)2 * 0.5 * 0.5

=66358

Sample size = 66358