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In: Statistics and Probability

A random sample of 200 high school students in a particular town showed that 122 smoke...

A random sample of 200 high school students in a particular town showed that 122 smoke on a regular basis. Find the 99% confidence interval estimating the population percentage for smokers at this high school.

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Expert Solution

Solution :

Given that,

n = 200

x = 122

Point estimate = sample proportion = = x / n = 122/200 = 0.610

1 - = 0-0.610 = 0.390

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

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

= 2.576 * ((0.610*(0.390) /200 )

= 0.089

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.610-0.089 < p < 0.610+0.089

0.521 < p < 0.699  

( 0.521. 0.699 )

orchestra answered 2 years ago
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