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 1042 tenth graders is drawn. Of the students sampled, 865 read above the eighth grade level. Using the data, construct the 90% 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 :

Sample size ( n ) = 1042

Fraction of tenth grade students that have reading skills ( x ) = 865

p = Propertion of tenth grade reading

q = 1- = 1- 0.8301 =0.1699

To find : 90 % confidence interval for population propertion

Now,

( 1- ) 100 % confidence interval for population propertion is given by,

So,

90 % confidence interval for population propertion of tenth grade reading is,

= = = 1.64 ......( From Z table )

=

=

=

=

= ( 0.811056 , 0.849212 )

= ( 0.811 , 0.849 )

90 % Confidence interval for the population propertion of tenth grade reading at or below the eight grade level is ( 0.811, 0.849 )