Question

In 2016, the Pew Research Center surveyed 1,799 white and 1,001 black Americans about their views on race and inequality. Pew researchers found “profound differences between black and white adults in their views on racial discrimination, barriers to black progress and the prospects for change.” White and black respondents also disagreed about the best methods to achieve racial equality. For example, 34% of whites and 41% of blacks said that “bringing people of different racial backgrounds together to talk about race” would be a very effective tactic for groups striving to help blacks achieve equality.

Test whether the proportion of white respondents who support this tactic is significantly less than the proportion of black respondents.

Calculate the Z statistic and test the hypothesis at the 0.05 level. What is the Z Statistic?

1. 3.50

2. -3.50

3. 0.0004

4. 0.07

Answer 1

p̂1=x1/n1 =	0.3400	p̂2=x2/n2 =	0.4100
n1                       =	1799	n2                       =	1001
estimated prop. diff =p̂1-p̂2    =		-0.0700
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.3650
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0200
test stat z=(p̂1-p̂2)/Se =		-3.500