Question

the State education commission wants to estimate the fraction of 10 greater students that have reading skills at or below the eighth grade level. Step 2 of 2 suppose a sample of 748 tenth graders is strong. Other students sampled. 187 read at or below the eighth grade level. Using the data, construct the 80% confidence interval for the population proportion of 10th graders reading at or below the eighth grade level. Round your answer to three decimal places.

Answer 1

Sample proportion = 187 / 748 = 0.25

80% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.25 - 1.2816 * sqrt [ 0.25 ( 1 - 0.25) / 748] < p < 0.25 + 1.2816 * sqrt [ 0.25 ( 1 - 0.25) / 748]

0.230 < p < 0.270

80% C I is ( 0.230 , 0.270 )