Question

In: Statistics and Probability

The state education commission wants to estimate the fraction of tenth grade students that have reading...

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.

Solutions

Expert Solution

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 )


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