Claire Lewis is running for mayor in her local town for the first time. The town
ID: 3338971 • Letter: C
Question
Claire Lewis is running for mayor in her local town for the first time. The town’s newspaper reports that a recent random sample showed that 180 out of 350 town residents support her. The 95% confidence interval for the proportion of town residents that support her is (0.4619, 0.5667). What does the 95% confidence interval tell you about the proportion of the town’s residents that support Claire?
Select all that apply:
A. 95% of the town’s residents support Claire Lewis for mayor.
B. 95% of the 350 residents sampled support Claire Lewis for mayor.
C. If we were to draw random samples over and over again, 95% of the confidence intervals would capture the true proportion of residents that support Claire for mayor.
D. There is a 95% chance that the true proportion of residents that support Claire Lewis is between 0.4619 and 0.5667.
E. There is a 95% chance that this is one of the samples where the true population proportion is within the confidence interval.
Explanation / Answer
P(0.4619<=p<=0.5667) = 0.95
It means the probability that the true proprtion of residents that support Claire Lewis lies between 0.4619 and 0.5667 is 0.95.
In other words, the probability that this is a sample where the true population proportion lies between 0.4619 and 0.5667 is 0.95.
Hence, option D and E are correct.