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 811 tenth graders is drawn. Of the students sampled, 137 read at or below 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 811 tenth graders is drawn. Of the students sampled, 137 read at or below the eighth grade level. Using the data, construct the 98% 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

Since n=811 is the sample of tenth grade drawn and x=137 read at or below the eighth grade level hence

the sample proportion

Step2.

The confidence interval at 98 % confidence interval is calculated as

={0.138, 0.200}

The z score is computed using Z tabl;e shown below