Question

A newspaper reports that the proportion of people that believe a governor is handling a certain situation well as 46% approval. There were 800 people surveyed. You were asked to report a 95% confidence interval around this proportion.

Interpret this confidence interval

Answer 1

Answer: A newspaper reports that the proportion of people that believe a governor is handling a certain situation well as 46% approval. There were 800 people surveyed. You were asked to report a 95% confidence interval around this proportion.

Solution:

n = 800

p = 46% = 0.46

At 95% confidence interval, α = 0.05

Z critical =Zα/2 = 1.96

the 95% confidence interval :

CI = p ± Z critical * √p(1-p)/n

CI = 0.46 ± 1.96 * √0.46(1-0.46)/800

CI = 0.46 ± 0.0345

CI = (0.4255, 0.4945)

Therefore, the 95% confidence interval is between 0.4255 and 0.4945.

With 95% confidence you conclude that governor handling a certain situation is between 43% and 49%.