Sample means, margin of error and confidence intervals

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Jun's random sample of 625 students found 52% want a longer lunch. Using the margin 1/√n, what is the upper end of the interval, as a percent?

   56
2. 2.

   Kira reads a state report: a random sample of 10,000 students found 63% recycle at home. Using the margin 1/√n, what is the upper end of the interval, as a percent?

   64
3. 3.

   Luz's random sample of 400 students found 71% read every day. Using the margin 1/√n, what is the lower end of the interval, as a percent?

   66
4. 4.

   Milo wants a margin of error of 4% for a district survey about lunch. Using the margin 1/√n, how many students should be in the random sample?

   625
5. 5.

   Pia wants a margin of error of 2.5% for a state survey about recycling. Using the margin 1/√n, how many students should be in the random sample?

   1600
6. 6.

   Ren's random sample of 200 students gave a margin of error of 6%. About how many students would give a margin of 3%?

   800
7. 7.

   Tala's random sample of 150 students gave a margin of error of 8%. About how many students would give a margin of 4%?

   600
8. 8.

   Zee's random sample of 100 students found 56% want a longer recess. Using the margin 1/√n, does it show that more than half of all the students do?

   • No: the interval 46% to 66% includes 50%, so it may not be more than half.
   • Yes: the whole interval 55% to 57% is above 50%.
   • Yes: 56% is more than 50%.
9. 9.

   Ari's random sample of 400 students found 46% walk to school. Using the margin 1/√n, does it show that fewer than half of all the students do?

   • Yes: the whole interval 45.75% to 46.25% is below 50%, so fewer than half do.
   • Yes: 46% is less than 50%.
   • No: the interval 41% to 51% includes 50%, so it may not be fewer than half.
10. 10.

    Bo reads a state report: a random sample of 10,000 students found 51.5% recycle at home. Using the margin 1/√n, does it show that more than half of all the students do?

    • Yes: the whole interval 50.5% to 52.5% is above 50%.
    • Can't tell: only asking every student could show it.
    • No: the interval 49.5% to 53.5% includes 50%, so it may not be more than half.