Question

GenForward is a well-conducted monthly survey of racially and ethnically diverse young American adults, aged 18-30. A recent poll asked respondents whether they believe President Donald Trump is a racist. 411 out of 775 Whites said yes, while 1670 out of 2161 people of color (Blacks, Asian or Hispanic) said yes. The following is a 95% confidence interval for p1-p2: (-0.28, -0.20). Which of the following is correct about the percentage of Americans in this age group who believe President Donald Trump is a racist?
a) People of color are between 20% and 28% more likely to say yes than Whites.
b) There is no significant difference in the proportion of people of color and White young adults who would answer yes to this question in the population.
c) A significance test to compare the proportion of people of color and Whites in the population who would answer yes to the question is expected to have a p-value larger than 0.05.
d) All of the above
e) None of the above

Answer 1

p1 is the proportion of people of Whites who believe President Donald Trump is a racist

p2 is the proportion of people of color who believe President Donald Trump is a racist

95% confidence interval for p1-p2: (-0.28, -0.20) --> I am 95% confident that the estimated difference in the population proportion of people of Whites and color who believe President Donald Trump is a racist lie in the interval (-0.28, -0.20).

Since this confidence interval doesn't contain 0, I reject the null hypothesis that there is no significant difference in the proportion of people of color and White young adults who would answer yes to this question in the population. hence "b) There is no significant difference in the proportion of people of color and White young adults who would answer yes to this question in the population." is wrong.

Since the confidence interval doesn't contain 0, the corresponding p-value is expected to be less than 0.05. This is because if p<5%, the null hypothesis rejected and the corresponding confidence interval doesn't contain 0. Thus, "c) A significance test to compare the proportion of people of color and Whites in the population who would answer yes to the question is expected to have a p-value larger than 0.05." is wrong.

Since the confidence interval contains all values less than 0, I can say that the population proportion of people of Whites who believe President Donald Trump is a racist is less than the population proportion of people of color who believe President Donald Trump is a racist. hence correct option is "a) People of color are between 20% and 28% more likely to say yes than Whites."