Question

Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 500 elementary school children and finds that 250 have a social media account. Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

Answer 1

Solution :

Given that,

n = 500

x = 250

Point estimate = sample proportion = = x / n = 250/500=0.5

1 - = 1-0.5=0.5

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 (((0.5*05) /500 )

E= 0.0576

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5 -0.0576 < p <0.5 + 0.0576

0.4424< p < 0.5576

The 99% confidence interval for the population proportion p is : 0.4424,0.5576