Confidence intervals from a sample, for averages and for percents
Grade 11 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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?
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?
In Esme's random sample of 100 bikes at school, a proportion 0.2 have bells (ring ring). Using 1.96, what is the upper end of the 95% interval, as a percent?
For the same n, which sample proportion gives Kira the widest interval?
- p = 0.1
- p = 0.5
- p = 0.9
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
- Disagree: it's about the mean
- Agree: 7.6 is the smallest
Noah's 95% interval for mean homework time is 40 to 50 minutes. Noah says nearly every student does 40 to 50 minutes. Agree or disagree?
- Agree: the interval holds the data
- Agree: 95% means nearly the whole class
- Disagree: single students vary more
Pia says a bigger sample always makes the interval wider. Agree or disagree?
- Agree: n is in the margin
- Disagree: it gets narrower
- Agree: more data, more spread
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%
Tala's 95% interval for mean ride time is 33.04 to 36.96 minutes. Is a true mean of 35 minutes believable?
- Yes: it's inside the interval
- No: 33.04 is the one possible value
- No: it must equal an end
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