In a random sample of 125 students, you find that 15 have tattoos (that’s 12%). Construct...

In a random sample of 125 students, you find that 15 have tattoos (that’s 12%). Construct a 95% confidence interval for the true population proportion of students that have tattoos.

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Expert Solution

Solution :

Given that,

n = 125

x = 15

Point estimate = sample proportion = = x / n =0.12 given

1 - = 1-0.12 =0.88

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= 1.96 ( $\sqrt$ ((0.12*0.88) /125 )

E = 0.057

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.12-0.057 < p < 0.12+0.057

0.063<p<0.177

orchestra answered 1 year ago

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