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 383 tenth graders is drawn. Of the students sampled, 84 read at or below the eighth grade level. Using the data, construct the 85% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

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Asked Dec 8, 2019
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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 383 tenth graders is drawn. Of the students sampled, 84 read at or below the eighth grade level. Using the data, construct the 85% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

 
 
 
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Expert Answer

Step 1

The proportion of tenth graders reading at or below the eighth grade level is calculated below:

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84 383 = 0.219 Thus, the proportion of tenth graders reading at or below the eighth grade level is 0.219.

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Step 2

The 85% confidence interval for the proportion of tenth gra...

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p(1– p) p±za (0.219×0.781) = 0.219 ±1.440, 383 = 0.219 ±1.440(0.021) = 0.189,0.249

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