Question

2. What percentage of adults in US are in favor of death penalty?
In a Gallup poll, 33 out of 50 randomly selected US adults said they are in favor of death penalty for a person convicted of murder. The bootstrap distribution shows that SE = 0.0661. Find and interpret a 99% confidence interval for the proportion of all US adults who are in favor of death penalty for a person convicted of murder. Show all steps to receive full credit.

Answer 1

Solution :

Given that,

n = 50

x = 33

Point estimate = sample proportion = = x / n = 33/50=0.66

1 -   = 1- 0.66 =34

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

=Z/2   * SE

= 2.576*0.0661

E = 0.17

A 99% confidence interval is ,

- E < p < + E

0.66 -0.17 < p < 0.66+0.17

(0.49 , 0.83)