According to a recent study by the Annenberg Foundation, only 36% of adults in the United States could name all three branches of government. This was based on a survey given to a random sample of 1416 U.S. adults.

a. Construct and interpret a 90% confidence interval for the proportion of all U.S. adults who could name all three branches of government.

b. Does the interval from part (a) provide convincing evidence that less than half of all U.S. adults could name all three branches of government? Explain your answer.