In a survey of 7000 women 4431 say they change their nail polish once a week. Construct a 90% confidence interval for the population proportion of women who cha

Question

in a survey of 7000 women 4431 say they change their nail polish once a week. Construct a 90%  interval for the population proportion of women who change their nail polish once a week.

Answer 1

I'll get you started.

 

The point estimate (which is the midpoint of the interval) is p=4431/7000.

 

For a 90% interval you need to find the z-value (say z₁₎ which will give the area under the normal curve between zero and z₁ of .45 (1/2 of .90 which you would use for a 90% interval.

 

You need to use the formula (p - z₁*σ_{p ,} p + z₁*σ_p) for the interval. P we calculated above, z₁ you got from the table, and σ_p = √p(1-p)/7000.