One of the findings after the 2016 U.S. Presidential election was that polls tended to have an over-representation of those with college degrees. This kind of overrepresentation may be due to selection bias (who is called) and/or non-response bias (who answers the phone). In this problem, we’ll look at how it could come about through non-response bias. Data for the problem is loosely based on voter registration data from Allegheny County in Pennsylvania. Suppose a particular county contains 950,000 registered voters. 380,000 of them (40%) have college degrees and 570,000 of them (60%) do not. Among those with college degrees, 304,000 (80%) support the Democratic candidate in a presidential election. Among those without college degrees, 313,500 (55%) support the Democratic candidate. (a) Based on this information, what percent of all registered voters in the county support the Democratic candidate? _____% In reality, of course, we would not know what percent of these voters supported the Democratic candidate; we’d have to collect data about it. Suppose that the phone numbers of all 950,000 registered voters were available and that a polling organization choses some of them at random to call. (b) If 8% of those with college degrees and 4% of those without college degrees will answer their phones, but these rates do not depend on which candidate the voter supports, then what is the chance that someone who DOES answer the phone supports the Democratic candidate? _____%
One of the findings after the 2016 U.S. Presidential election was that polls tended to
have an over-representation of those with college degrees. This kind of overrepresentation may be due to selection bias (who is called) and/or non-response bias
(who answers the phone). In this problem, we’ll look at how it could come about
through non-response bias. Data for the problem is loosely based on voter registration
data from Allegheny County in Pennsylvania.
Suppose a particular county contains 950,000 registered voters. 380,000 of them (40%)
have college degrees and 570,000 of them (60%) do not. Among those with college
degrees, 304,000 (80%) support the Democratic candidate in a presidential election.
Among those without college degrees, 313,500 (55%) support the Democratic
candidate.
(a) Based on this information, what percent of all registered voters in the county
support the Democratic candidate? _____%
In reality, of course, we would not know what percent of these voters supported the
Democratic candidate; we’d have to collect data about it. Suppose that the phone
numbers of all 950,000 registered voters were available and that a polling organization
choses some of them at random to call.
(b) If 8% of those with college degrees and 4% of those without college degrees will
answer their phones, but these rates do not depend on which candidate the voter
supports, then what is the chance that someone who DOES answer the phone
supports the Democratic candidate? _____%
(Hint: First find the number of those with and without college degrees who will
answer their phones. Now find the number within each of these groups who support
the Democratic candidate. Can you put this information together to answer the
question?)
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