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A random sample of 150 preschool children in Hillsborough county revealed that only 60 had been...

A random sample of 150 preschool children in Hillsborough county revealed that only 60 had been vaccinated. Provide an approximate 95% confidence interval for the proportion vaccinated in that county.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 60 / 150 = 0.4

Z/2 = 1.96

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

= 1.96 * (((0.4 * 0.6) / 150)

= 0.078

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4 - 0.078 < p < 0.4 + 0.078

0.322 < p < 0.478

(0.322 , 0.478)

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