6) A poll conducted by Pew Research asked a random sample of 1300 adults in the U.S. how much confidence they had in banks and other financial institutions. A total of 169 adults said they had a great deal of confidence in these institutions. An economist claims it is less than 15%. Test the economist's claim at $\alpha = .05$.
a) State $H_0$ and $H_a$
b) Find the critical value, show work
15 points
c) Find the appropriate test statistic, and show all values used in formula
d) Do a P - value test
e) Make a decision to reject or fail to reject the null hypothesis and interpret the results.