Confidence intervals from a sample, for averages and for percents

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   In Ari's random sample of 400 students, a proportion 0.4 want a later start. Using 1.96, what is the upper end of the 95% interval, as a percent?

   44.8 %
2. 2.

   In Bo's random sample of 100 shoppers, a proportion 0.5 bring their own bags. Using 1.96, what is the upper end of the 95% interval, as a percent?

   59.8 %
3. 3.

   Jun's sample of 100 has p = 0.50. What is the 95% margin of error?

   • 5 percentage points
   • 50 percentage points
   • 9.8 percentage points
4. 4.

   For the same n, which sample proportion gives Kira the widest interval?

   • p = 0.5
   • p = 0.9
   • p = 0.1
5. 5.

   Luz's sample of 400 has p = 0.40. What is the 95% interval?

   • 35% to 45%
   • 35.2% to 44.8%
   • 39.9% to 40.1%
6. 6.

   Milo's 95% interval for mean sleep is 7.6 to 8.2 hours. Milo says 95% of students sleep 7.6 to 8.2 hours. Agree or disagree?

   • Agree: 95% of the data lie inside
   • Agree: 7.6 is the smallest
   • Disagree: it's about the mean
7. 7.

   Pia says a bigger sample always makes the interval wider. Agree or disagree?

   • Agree: more data, more spread
   • Agree: n is in the margin
   • Disagree: it gets narrower
8. 8.

   Ren's 95% interval is 35.2% to 44.8%. Someone claims half of all students want a later start. Is that believable?

   • No: 50% is outside the interval
   • Yes: 50% is close enough to count
   • Yes: 40% rounds to 50%
9. 9.

   Tala's 95% interval for mean ride time is 33.04 to 36.96 minutes. Is a true mean of 35 minutes believable?

   • No: 33.04 is the one possible value
   • No: it must equal an end
   • Yes: it's inside the interval
10. 10.

    Class A's interval is 60% to 70% and class B's is 75% to 85%. What does Zee conclude?

    • A's true percent is likely higher
    • B's true percent is likely higher
    • They are surely the same