Individuals who enrolled in Affordable Care Act Heath Insurance Marketplace plans represented about 4.1% of all Americans with insurance in 2015. The Department of Health & Human Service wanted to determine whether the rate of enrollment in these marketplace plans in 2016 grew as compared to the 2015 rate of 4.1%. It selected a random sample of 500 insured Americans in 2016 and found that 29 of them enrolled in ACA marketplace plans.

1. Could the Department of Health & Human Service be reasonably sure that the enrollment rate increased? Calculate a p-value for the observed proportion and interpret it.
2. If the significance level is set at .01, is this change in enrollment rate statistically significant? State your hypotheses and conduct a test.