Question

A 2010 headline stated that "73% say Woman President Likely in the next 10 years." The report gives the results of a survey of 1000 randomly selected likely voters in the US. Find and interpret a 95% confidence interval for the proportion of likely voters in the US in 2010 who thought a woman president is likely in the next 10 years.

Answer 1

Solution :

Given that,

n = 1000

Point estimate = sample proportion = =73%=0.73

1 -   = 1- 0.73=0.27

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 = 1.96   ( Using z table )

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

= 1.96 (((0.73*0.27 /1000 )

= 0.028

95% confidence interval for the proportion

- E < p < + E

0.73 - 0.028 < p < 0.73+0.028

0.702< p < 0.758

interpret a 95% confidence interval for the proportion of likely voters in the US in 2010 who thought a woman president is likely in the next 10 years (0.702 , 0.758)