Question

A simple random sample of 400 individuals provides 100 Yes responses.

a. What is the point estimate of the proportion of the population that would provide Yes responses? (to 2 decimals)

later use p-- rounded to 2 decimal places

b. What is your estimate of the standard of error of the proportion? ( to 4 decimals)

c. Compute the 95% confidence interval for the population proportion. (to 4 decimals)

MUST INCLUDE:

The knowns

Graphs

Formulas

Steps to Solve

Box the Answer

Answer 1

Solution:

Given( Known's) :

Sample Size = n = 400

x = Number of individuals provides Yes responses = 100

Part a) the point estimate of the proportion of the population that would provide Yes responses:

Formula:

Thus point estimate of population proportion is:

Part b) An estimate of the standard of error of the proportion:

Formula:

Part c) Compute the 95% confidence interval for the population proportion.

Formula:

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus