Question

n 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States

Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this view has decreased since 2005? Test this claim at the 5% significance level.

Let p be the proportion of U.S. adults in 2015 who have confidence in the U.S. Congress.

What is the standardized test statistic? Round to two decimal places.

Answer 1

P = X / n = 21/145 = 0.1448
Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.1448 - 0.2 ) / ( √(( 0.2 * 0.8) /145))
Z = -1.66