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A recent survey of 349 people ages 18 to 29 found that 86% of them own...

A recent survey of 349 people ages 18 to 29 found that 86% of them own a smartphone. Find the 99% confidence interval of the population proportion.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

n = 349

Point estimate = sample proportion = = 0.86

1 - = 1 - 0.86 = 0.14

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 (((0.86 * 0.14) / 349)

= 0.048

A 99% confidence interval for population proportion p is ,

± E  

= 0.86  ± 0.048

= ( 0.812, 0.908 )

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