Question

Determine the necessary sample size for the following examples:

A) A senator wants an estimate of the proportion of the population who support her education views. She wants the estimate to be within .013 of the true proportion. Assume a 95 percent level of confidence.

B) 45 percent of tourists going to Las Vegas go to a concert. The Las Vegas tourism board wants to update this percentage. For the new study, the estimate should be within 2% of the population proportion with a 98 percent confidence level.

Answer 1

Solution:

a ) Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.013

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.013)² * 0.5 * 0.5

= 5682.898

= 5683

n = sample size = 5683

b ) Given that,

= 40% =0.45

1 - = 1 - 0.45 = 0.55

margin of error = E = 2% = 0.02

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= (2.326/ 0.02)² * 0.45 * 0.55

= 3347.6082

= 3348

n = sample size = 3348