Question

In a survey of

six thousand

​women,

3431

say they change their nail polish once a week. Construct a

ninety five percent

confidence interval for the population proportion of women who change their nail polish once a week.

A

ninety five percent

confidence interval for the population proportion is

(__,___).

round to the 3 decimal places if it is needed.

.13

Answer 1

Solution :

n = 6000

x = 3431

= x / n = 3431 / 6000 = 0.572

1 - = 1 - 0.572 = 0.428

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (((0.572 * 0.428) /6000)

  = 0.012

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.572 - 0.012 < p < 0.572 + 0.012

0.560 < p < 0.584  

( 0.560,0.584 )