Question

In March 1999, the Gallup Organization conducted a survey among 535 adults and asked them if they believed there is some form of life on other planets in the universe. In another survey conducted three years earlier, among 535 adults the same questions was asked. The results appear below:

	1999	1996	Difference
Yes	326	385	-59
No	209	150	59
Sample Size	535	535	535

Calculate the 95% confidence interval for the difference in response. Interpret your confidence interval.

Answer 1

(1)

n1 = 535

p1 = 326/535 = 0.6093

n2 = 535

p2 = 385/535=0.7196

Q =1 - P = 0.3355

=0.05

From Table, critical values of t = 1.96

Confidence Interval:

(0.6093 -0.7196) (1.96 X 0.0289)

= - 0.1103 0.0566

= (- 0.1669 , - 0.0537)

Confidence Interval:

- 0.1669 < P1 - P2 < - 0.0537

(2)

Interpretation:

The 95% confidence interval for difference in proportions: - 0.1669 < P1 - P2 < - 0.0537 is a range of values that is likely to contain the population proportion difference. If we conduct the experiment many times and each time confidence interval for difference in proportions is calculated, 95% of the confidence intervals ill contain the population propulation proportion difference.