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 1 of 2:

Suppose a sample of 2751 tenth graders is drawn. Of the students sampled, 2146 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 2751 tenth graders is drawn. Of the students sampled, 2146 read above 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. Find Lower and Upper Endpoint

Answer 1

a)

Number of students read below eighth grade level = 2751 - 2146 = 605

Proportion of tenth graders reading at or below the eighth grade level = = 605 / 2751 = 0.220

b)

99% confidence interval for p is

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

0.220 - 2.5758 * sqrt [ 0.220 ( 1 - 0.220) / 2751 ] < p < 0.220 +2.5758 * sqrt [ 0.220 ( 1 - 0.220) / 2751 ]

0.200 < p < 0.240

Lower endpoint = 0.200

Upper endpoint = 0.240