Question

# A random sample of 125 people shows that 25 are left-handed. Form a 99% confidence interval...

A random sample of 125 people shows that 25 are left-handed. Form a 99% confidence interval for the true proportion of left-handers.

Solution :

Given that,

Point estimate = sample proportion = = x / n = 25 / 125 = 0.20

1 - = 1 - 0.20 = 0.80

Z /2 = Z0.005 = 2.576

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

= 2.576 ( ((0.20 * 0.80) / 125)

= 0.092

A 99% confidence interval for population proportion p is , ± E

= 0.20  ± 0.092

= ( 0.108, 0.292 )

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