Question

Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary school children and finds that 280 have a social media account.

Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

• Round the final answer to three decimal places.

Answer 1

SOLUTION:

From given data,

Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary school children and finds that 280 have a social media account.

Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

P = 280/450 = 0.622

N = sample size = 450

Standard deviation() = sqrt( {p*(1-p)}/ n )

  = sqrt( {0.622*(1-0.622)}/ 450 )

= 0.0228578214184

= 0.023

99% confidence level

Confidence level is 99%

99% = 99/100 = 0.99

= 1 - Confidence interval = 1-0.99 = 0.01

/2 = 0.01 / 2

= 0.005

Z_/2 = Z_0.005  = 2.576

Margin of error = Z_/2 *

= 2.576*0.023

   MOE = 0.05934

Confidence interval is given by

(p-MOE, p+MOE)

(0.622-0.05934, 0.622+0.05934)

(0.56266, 0.68134)

(0.563, 0.681) (rounded the answer for three decimal values)