Question

Find the sample size needed to estimate the percentage of residents of one region of a country who are​ left-handed. Use a margin of error of four percentage points​, and use a confidence level of 99​%. Complete parts​ (a) through​ (c) below. a. Assume that ModifyingAbove p with caret and ModifyingAbove q with caret are unknown. The sample size needed is nothing. ​(Round up to the nearest whole number as​ needed.)

Answer 1

Given:

Margin of error, E = 4% = 0.04

Significance level, = 1-0.99 = 0.01

At 99% significance level, the critical value of Z is

Z/2 = Z0.01/2 = Z0.005 = 2.58

Also given that

Assume that Modifying Above p with caret and Modifying Above q with caret are unknown.

So = 0.5 and = 1- = 1-0.5 = 0.5

From the margin of error formula, we find the sample size.

So sample size is

n = (Z/2 / E)^2 * * (1 - )

= (2.58/0.04)^2 * 0.5 * (1-0.5)

= (2.58/0.04)^2 * 0.25

= 1040.06

= 1040 ....(try 1036 if getting wrong )

So the required sample size is n = 1040

answered by: anonymous