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 333 tenth graders is drawn. Of the students sampled, 254 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

Solution :

Given that,

n = 333

x = 254

Point estimate = sample proportion = = x / n = 254 / 333 = 0.763

1 - = 1 - 0.763 = 0.237

At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z0.10  = 1.282

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.282 (((0.763 * 0.237) / 333 )

= 0.030

A 80% confidence interval for population proportion p is ,

± E  

= 0.763  ± 0.030

= ( 0.733, 0.793 )