Question

Of the first 100 appointments to the nation’s Supreme Court, 52% of the justices have been firstborn or only children. Assuming the 100 Supreme Court justice appointments represent a random sample of all past and future justices, construct a 95% confidence interval for the percentage of all Supreme Court justices who were firstborn or only children.

Answer 1

Solution :

Given that,

n = 100

Point estimate = sample proportion = = 0.52

1 -   = 1- 0.52 =0.48

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    * ((( * (1 - )) / n)

= 1.96 (((0.52*0.48) /100 )

= 0.0979

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.52-0.0979 < p < 0.52+ 0.0979

0.4221< p < 0.6179

The 95% confidence interval for the population proportion p is : 0.4221,0.6179