Question

The state education commission wants to estimate the fraction of tenth grade students that have reading...

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.

Homework Answers

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)

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