Rework Exercise 7 using the alternative formula and verify that the results are the same.

Data from Exercise 7:

A medical researcher says that less than 80% of U.S. adults think that healthy children should be required to be vaccinated. In a random sample of 200 U.S. adults, 82% think that healthy children should be required to be vaccinated. At α = 0.05, is there enough evidence to support the researcher’s claim?

(a) Identify the claim and state H₀ and H_a, 

(b) Find the critical value(s) and identify the rejection region(s), 

(c) Find the standardized test statistic z, 

(d) Decide whether to reject or fail to reject the null hypothesis, and 

(e) Interpret the decision in the context of the original claim.