12th grade Read election and census data: turnout, apportionment and margins of error worksheet

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?

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

   A writer says citizen turnout rose by at least 4 points from 2016 to 2020. Bo checks the claim against cards A to C. What is the best verdict?

   • Not supported: the margins add to 0.7, so the 5.4-point rise could be as small as 4.7 points, which is not clearly above 4
   • Supported: the margins are small, so the rise is exactly 5.4 points and cannot be anything else
   • Not supported: both figures are what people said, not what they did, so the true rise could be zero or below
   • Supported: the rise is 5.4 points and the combined margin is about half a point, so the rise stays above 4
4. 3.

   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
   • 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
   • Cannot be judged: the 18 to 24 margin of 1.2 is larger than any difference printed on the cards
5. 4.

   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?

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

6. 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.

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?

   • 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
   • Sampling error: a margin of 2.5 means estimates can miss by 5 points, so the survey and the records agree
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?

   • Right: a doubled sample halves the margin to 0.2 and also removes the bias that comes from who answers and how
   • Right: a bigger sample cuts bias because it reaches the people who gave no response in the first round
   • Partly right: the margin would shrink, but not by half, and bias from self-reports and nonresponse would stay
   • Wrong: a larger sample cannot lower a margin of error, because the margin depends on who is surveyed
9. 7.

   A writer says 2020 citizens 65 to 74 voted at a higher rate than those 18 to 24. Ren tests it against the nonresponse figures on card A. What is the best verdict?

   • Cannot be judged: nonresponse of 19.3 and 13.9 percent could move either rate by more than the gap does
   • Supported: the 24.6-point gap is larger than the combined margin, so nonresponse cannot matter to the ranking
   • Supported: even if every 18 to 24 nonrespondent voted and no 65 to 74 nonrespondent did, the younger rate stays lower
   • Refuted: 18 to 24 had more nonresponse, so its true rate is higher than reported and above the older rate

10. 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.

11. 8.

    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
    • New York's seat ranked above Minnesota's, but the Bureau gave the last seat to the smaller state anyway
    • New York's 27th seat ranked 436th, just behind Minnesota's 435th, so a tiny change in either count could swap them
    • 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
12. 9.

    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
    • No: its priority value would fall 2 percent, below 762,997.7, since it led that value by under 1 percent
    • 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
13. 10.

    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