Confidence interval for a population proportion Suppose a graduate student in political science is interested in determining the proportion of voting adults in her community who identify as liberal. She believes that the proportion of the 2,543 voting adults in the community who identify as liberal is about 0.57. To investigate this claim, she selects a random sample of 225 voting adults and constructs a confidence interval for the proportion of voting adults in the community who identify as liberal.

(a) The sample produces a total of 146 voting adults who identify as liberal . The proportion of adults in the sample who are liberal is p = 0.65

(b) The standard error of the sample proportions, or SEP, is 0.03182

(c) You can be 95% confident that the interval 0.58600 @ to 0.71100 @ includes the population proportion p. (Hint: For a 90% confidence interval, use 1.645 as the multiplier. For a 95% confidence interval, use 1.960. For a 99% confidence interval, use 2.576.) Since the confidence interval for p contains X 0.57, the evidence provided by the sample data is not X strong enough to reject the graduate student's claim.