Question

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Step 2 of 2:

Suppose a sample of 1223 tenth graders is drawn. Of the students sampled, 232 read at or below the eighth grade level. Using the data, construct the 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

Answer 1

n=1223 x=232

p=x/n=1223/232=0.19

99 %  confidence interval for the population proportion is

- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)

# z critical value for 99 % cofidence is

=1-c%=1-0.99=0.01

Z/2=Z0.025=2.5758

0.19 - 2.5758 * sqrt( 0.19 * 0.81 / 1223) < p <0.19 +2.5758 * sqrt( 0.19 * 0.81 / 1223)

0.161< p < 0.219

99% conidence interval around estimate is (0.161, 0.219)