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. Suppose a sample of 292 tenth graders is drawn. Of students sampled, 240 read at or below 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 answer to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 240 / 292 = 0.822

1 - = 1 - 0.822 = 0.178

Z/2 = Z0.1 = 1.282

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

= 1.282 * (((0.822 * 0.178) / 292)

E = 0.029

A 80% confidence interval for population proportion p is ,

- E < p < + E

0.822 - 0.029 < p < 0.822 + 0.029

0.793 < p < 0.851

The 80% confidence interval for the population proportion p is : (0.793 , 0.851)