Question

1. A recent Gallup poll showed that 672 of 1019 adults nationwide think that marijuana should be legalized. a) Find the margin of error that corresponds to a 95% confidence interval. b.)Find the 95% confidence interval estimate of the proportion of adults nationwide who think marijuana should be legalized.

Answer 1

Solution:

Given,

n = 1019 ....... Sample size

x = 672 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 672 / 1019 = 0.6595

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now , the margin of error is given by

E = /2 *  

= 1.96 * [(0.6595*(1 - 0.6595)/1019]

= 0.0291

Now the confidence interval is given by

( - E)   ( + E)

(0.6595 - 0.0291 )   (0.6595 +  0.0291 )

0.6304    0.6886

Interval is (0.6304 , 0.6886 )