Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: nine percentage points; confidence level 90%; from a prior study, p hat is estimated by the decimal equivalent of 46%

Answer 1

Solution :

Given that,

= 46% = 0.46

1 - = 1 - 0.46 = 0.54

Margin of error = E = 9% = 0.09

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Sample size = (  Z_/2 / E)² * * (1 - )

= (1.645 / 0.09)² * 0.46 * 0.54

= 82.98

Sample size = n = 83