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 310 tenth graders is drawn. Of the students sampled, 46 read at or below the eighth grade level. Using the data, construct the 85% 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 = 46 / 310 = 0.148

= 1 - 0.85 = 0.15

From Z table,

Z/2 = 1.476

85% confidence interval for p is

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

0.148 - 1.476 * sqrt [ 0.148 ( 1 - 0.148) / 310 ] < p < 0.148 + 1.476 * sqrt [ 0.148 ( 1 - 0.148) / 310 ]

0.118 < p < 0.178

85% CI is ( 0.118 , 0.178 ) ​​​​​​​