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 313 tenth graders is drawn. Of the students sampled, 235 read above the eighth grade level. Using the data, construct the 80% 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

Sample proportion below 8th grade level = = (313 - 235) / 313 = 78/313 = 0.249

80% confidence interval for p is

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

0.249 - 1.2816 * sqrt( 0.249 * 0.751 / 313) < p < 0.249 + 1.2816 * sqrt( 0.249 * 0.751 / 313)

0.218 < p < 0.280

80% CI is ( 0.218 , 0.280 )