Read election and census data: turnout, apportionment and margins of error

Grade 12 Social Studies Worksheet - Challenge Me

Circle the best answer.

1. Read this first

   Use this

   Cards A to C on who said they voted in 2016 and 2020 (the figures are the Census Bureau's Current Population Survey, a sample survey; card C is in our words). Card A, "Voting and registration, November 2020". Who made it: the Census Bureau (Tables 1 and 1a, census.gov). For whom: the public. Why: to report who said they registered and voted. Citizens 18 and over, in thousands: 231,593 in all; 168,308 reported registered (72.7 percent); 154,628 reported voting (66.8 percent, margin of error 0.4); 40,561 reported not voting (17.5 percent); 36,404 gave no response about voting (15.7 percent). By age, percent of citizens who reported voting (margin of error in points): 18 to 24, 51.4 (1.2); 25 to 34, 60.3 (0.7); 35 to 44, 65.1 (0.6); 45 to 54, 69.0 (0.5); 55 to 64, 72.7 (0.4); 65 to 74, 76.0 (0.4); 75 and over, 72.3 (0.4). No response about voting, percent of citizens: 18 to 24, 19.3; 65 to 74, 13.9. Card B, "Voting and registration, November 2016". Same maker, readers and aim. Citizens 18 and over, in thousands: 224,059 in all; 157,596 reported registered (70.3 percent); 137,537 reported voting (61.4 percent, margin of error 0.3). By age, percent of citizens who reported voting (margin of error in points): 18 to 24, 43.0 (0.9); 25 to 34, 53.1 (0.6); 35 to 44, 60.2 (0.5); 45 to 54, 65.3 (0.4); 55 to 64, 67.9 (0.3); 65 to 74, 72.6 (0.3); 75 and over, 68.4 (0.3). Card C, "Margins of error" (in our words, not a quotation). The margin of error describes random sampling error in one estimate. To judge a difference between two independent estimates, combine their margins: the square root of the sum of the two squared margins. A difference smaller than the combined margin cannot be told apart from sampling error.

2. 1.

   Tala tests a writer's claim that turnout rose more among citizens 75 and over than among those 65 to 74, using cards A to C. What is the best verdict?

   • Supported: 75 and over rose by more, and each rise is larger than any single margin of error printed on the cards
   • Refuted: citizens 65 to 74 had the higher turnout in both years, so their turnout must have risen more
   • Not supported: the two rises differ by half a point, which is within the combined margins of the four estimates
   • Not supported: margins of error apply to a single year, so rises between years cannot be compared
3. 2.

   A writer says the turnout gap between citizens 18 to 24 and 65 to 74 narrowed from 2016 to 2020. Noah tests it with cards A to C. What is the best verdict?

   • Supported: the gap fell from about 30 points to about 25, more than the margins explain, but a large gap remains
   • Cannot be judged: the 18 to 24 margin of 1.2 is larger than any difference printed on the cards
   • Refuted: older citizens' turnout also rose between the two elections, so the gap could not have narrowed
   • Supported: the gap closed, so young and older citizens now vote at similar rates in national elections
4. 3.

   A writer says young adults in 2020 vote as older adults did in 2016, citing 60.3 and 60.2. Esme tests it with cards A to C. What is the best verdict?

   • Refuted: the two groups are different ages, so their rates cannot be compared with each other
   • Supported: card C says estimates within one point of each other are equal, so the age groups voted alike
   • Supported: the rates are 60.3 and 60.2, so the 2016 group and the 2020 group are the same voters at the same rate
   • Weakly supported: the rates match within the margins, but they describe different people, so the match shows no change over time

5. Use this

   Cards A to E on error and bias in a turnout survey (the figures on cards A and B are the Census Bureau's Current Population Survey; cards C and D are in our words; card E is made up). Card A, "Voting and registration, November 2020". Who made it: the Census Bureau (Tables 1 and 1a, census.gov). For whom: the public. Why: to report who said they registered and voted. Citizens 18 and over, in thousands: 231,593 in all; 154,628 reported voting (66.8 percent, margin of error 0.4); 40,561 reported not voting (17.5 percent); 36,404 gave no response about voting (15.7 percent). By age, percent of citizens who reported voting (margin of error in points): 18 to 24, 51.4 (1.2); 65 to 74, 76.0 (0.4). No response about voting, percent of citizens: 18 to 24, 19.3; 65 to 74, 13.9. Card B, "Voting and registration, November 2016". Same maker and aim. Citizens reporting voting: 61.4 percent (margin of error 0.3). Card C, "Margins of error" (in our words, not a quotation). The margin of error describes random sampling error in one estimate. It falls to half only if the sample grows fourfold. Card D, "Bias" (in our words, not a quotation). Bias comes from who is reached, who answers and how people report, so a larger sample does not remove it. Bias can push an estimate in one direction by more than its margin of error. Card E, "Larkin County (made up)". Who made it: written for this sheet. Summary in our words: Election records in Larkin County show that 61 percent of citizens cast ballots. A phone survey of 1,500 citizens there reports that 66 percent voted, with a margin of error of 2.5 points. About four in ten of the people called did not answer.

6. 4.

   A writer drops the 36,404,000 citizens with no voting response in 2020 and says 79 percent of the rest voted. Ari tests it with cards A to D. What is the best verdict?

   • Better than the Bureau's 66.8, since people who give no answer should not be counted as if they had not voted
   • Fine: dropping the no-response group lowers the margin of error, so the 79 percent is the more precise figure
   • Misleading: it assumes those who gave no response voted like those who answered, which the survey cannot show
   • Wrong by 12 points, so the margin of error of 0.4 supports the Bureau's figure and undermines the writer's figure
7. 5.

   Larkin County's records show 61 percent of citizens voted; a survey says 66 percent, with a margin of error of 2.5 points. Luz reads cards C to E. What best explains the gap?

   • Sampling error: a margin of 2.5 means estimates can miss by 5 points, so the survey and the records agree
   • The survey is biased if a campaign paid for it, since card D names that as the source of bias
   • The gap is twice the margin, so sampling error is unlikely; people overstating or nonvoters missing are likelier
   • The records are wrong: a survey of 1,500 people is more reliable than a count of the ballots cast
8. 6.

   The 2020 margin for all citizens is 0.4. A planner says doubling the sample would halve the margin and fix nonresponse bias. Kira tests this with cards C and D. What is the best verdict?

   • Wrong: a larger sample cannot lower a margin of error, because the margin depends on who is surveyed
   • Partly right: the margin would shrink, but not by half, and bias from self-reports and nonresponse would stay
   • Right: a bigger sample cuts bias because it reaches the people who gave no response in the first round
   • Right: a doubled sample halves the margin to 0.2 and also removes the bias that comes from who answers and how

9. Use this

   Cards A to D on how the 435 House seats are assigned (the figures are the Census Bureau's 2020 apportionment tables; card A is in our words). Card A, "The Method of Equal Proportions" (in our words, not a quotation). Each state first gets one seat. Each later seat goes to the state with the highest priority value, which is the state's apportionment population divided by the square root of n times (n minus 1), where n is the number of the seat the state would receive next. The Bureau lists the values in order; the 435th seat is the last one awarded. Card B, "Priority values for House seats 433 to 438". Who made it: the Census Bureau (2020 Census apportionment tables, census.gov). For whom: Congress and the states. Why: to show how each seat was assigned. Seat 433: California's 52nd seat, 768,516.9. Seat 434: Montana's 2nd seat, 767,498.7. Seat 435: Minnesota's 8th seat, 762,997.7. Seat 436: New York's 27th seat, 762,994.4. Seat 437: Ohio's 16th seat, 762,257.9. Seat 438: Texas's 39th seat, 758,071.5. Seats 436 and higher were not awarded. Card C, "Populations, 2020 Census". Who made it: the Census Bureau. Apportionment population: Montana 1,085,407; Minnesota 5,709,752; New York 20,215,751. Resident population: Montana 1,084,225; Minnesota 5,706,494; New York 20,201,249. Overseas personnel assigned to the state: Montana 1,182; Minnesota 3,258; New York 14,502. Total apportionment population 331,108,434; average 761,169 people per seat. Card D, "Two more states". Who made it: the Census Bureau. Texas: 29,183,290 people, 38 seats. California: 39,576,757 people, 52 seats.

10. 7.

    A story says New York lost the last House seat to Minnesota by a tiny margin. Milo reads cards A to C. Which statement is best supported?

    • Minnesota won the last seat because it grew faster than New York between the 2010 and 2020 censuses
    • The method gives the last seat to the smaller state of the two, since Minnesota's population is smaller than New York's, as card C shows
    • New York's 27th seat ranked 436th, just behind Minnesota's 435th, so a tiny change in either count could swap them
    • New York's seat ranked above Minnesota's, but the Bureau gave the last seat to the smaller state anyway
11. 8.

    Suppose Montana's apportionment count had been 2 percent lower. Zee applies cards A and B. Would Montana have kept its second seat?

    • Yes: a state's first seat is automatic, so its second seat could not be lost however its count changed
    • Yes: a 2 percent drop in population lowers the priority value by less than 1 percent, so the seat is kept
    • No: the seat would pass to Minnesota if New York also lost its place in the order of seats
    • No: its priority value would fall 2 percent, below 762,997.7, since it led that value by under 1 percent
12. 9.

    A writer says counting overseas personnel cost New York its 27th seat. Jun tests it with cards A to C. What is the best verdict?

    • Supported: the gap between the two priority values is just over 3, smaller than the change removing overseas personnel would cause
    • Not supported: removing overseas personnel lowers New York's priority value more than Minnesota's, widening Minnesota's lead
    • Not supported: overseas personnel are under 0.1 percent of either count, so excluding them could not alter any ranking
    • Cannot be judged: the cards give no priority values for New York or Minnesota computed without overseas personnel
13. 10.

    A student predicts each state's seats by rounding its apportionment population divided by 761,169. Pia tests the rule on Montana and New York with cards A to C. Where does it fail?

    • It fails for Minnesota, whose quotient of about 7.5 rounds to 7, while the method gave Minnesota 8, so the rule is off by one seat there
    • It gives New York 27 and Montana 1; the method gave New York 26 and Montana 2, since seats go by priority value, not rounding
    • It works for both states: the quotient of about 26.56 for New York rounds to 26, and about 1.43 for Montana rounds to 2
    • It fails for Texas, whose quotient of about 38.3 rounds to 39, while the method gave Texas 38, so the rule is off by one seat there