Download 13C1 - PowerPoint - Data Inferences - Day 1

Problem Solving and Data Analysis
13 – Data Inferences
Calculator Required
Day 1
Entrance Slip Discussion
1. A teacher wants to find the average height, in cm, of her seventh hour students. Is this a feasible
measurement to obtain? Justify your answer.
Yes, this information can be obtained. She can simply measure all the students and average the
heights.
2. A superintendent wants to find the average number of AP/Honors classes each student in the
district is currently taking. Is this a feasible measurement to obtain? Justify your answer.
Yes, this information can be obtained. The school district can run a report on AP/Honors classes
and computer the average.
3. A large shoe company wants to know the average shoe size for every person currently living in
the United States. If this a feasible measurement to obtain? Justify your answer.
No, this information cannot be obtained. There are too many people to contact and such a project
would be too expensive.
Because some information cannot be obtained, researchers will approximate the larger group using
a smaller sample.
When researchers cannot find the exact value and need to estimate using the results from a smaller
sample, there is some wiggle-room for the approximations. We call this wiggle-room the Margin of
Error.
A large shoe company wants to know the average shoe size for every person currently living in the
United States. To approximate this value, the company randomly selects 10,000 US residents and
records their shoe size. The average shoe size recorded is 9.7 with a margin of error of 1.1 at the
95% confidence level.
What they
want to know
(parameter)
Who they
want to know
about
(population)
What value
they found
(statistic)
Wiggle-room
(Marin of Error)
Who they ask
(sample)
The shoe company can estimate that the average for all people living in the US is: 9.7  1.1
Writing it like this can be confusing. Results are often given as a confidence interval.
The company estimates the average shoe size of people living in the United States to be between
8.6 and 10.8.
In a poll of 1,578 randomly selected American adults, 44.8% of the respondents said that airlines
should allow in-flight calls on airplanes. The poll reported a margin of error of 2.5% at a 95%
confidence level.
1. What is the value obtained through sampling (sample statistic)?
2. What is the margin of error?
44.8%
2.5%
3. Between which two values could the actual percentage for all American adults fall (confidence
interval)?
Between 42.3% and 47.3%
4. Select all that apply. Which of the following could be equal to the percentage of all American
adults who say that airlines should allow in-flight calls?
A. 40%
B. 43%
C. 45%
D. 48%
E. 95%
Based on random samples of river heights, oceanographers estimate that 4,800
3
cubic kilometers  km  of freshwater is discharged into the Arctic Ocean annually.
The estimate has a margin of error of 240km3 at the 90% confidence level. Which
of the following is the most reasonable claim about the volume of freshwater
discharged annually into the Arctic Ocean?
A. It is between 4,800 and 5,040 cubic km.
B. It is between 4,560 and 5,040 cubic km.
C. It is between 240 and 4,800 cubic km.
D. It is between 240 and 4,320 cubic km.
4800 – 240 = 4560
4800 + 240 = 5040
Prior to the 2014 elections, 1,000 randomly selected Louisiana voters were
surveyed about what single issue would most likely influence their vote. Of those
surveyed, 560 voters answered that the state of the economy would most influence
their vote. Based on this information, which statement about all voters in Louisiana
is most appropriate?
Estimation, not exact.
A. Exactly 56% of all Louisiana voters thought the state of the economy would
most influence their voting.
B. Approximately 56% of all Louisiana voters thought the state of the economy
would most influence their voting.
Exactly what they answered.
C. Exactly 56% of Louisiana voters would vote for the candidate with the best plan
to improve the economy.
D. Approximately 56% of Louisiana voters would vote for the candidate with the
best plan to improve the economy.
“Best plan” is subjective.
A random sample of 500 residents of a town included 173 residents who primarily
spoke a language other than English at home, with a margin of error of 25
residents and a confidence level of 98%. If the town has 25,000 residents, how
many residents primarily speak a language other than English at home, with a 98%
confidence level?
173
Sample Statistic =
 34.6%
A. 7,400 to 9,900 residents
500
25
Margin of Error =
 5%
500
B. 8,625 to 8,675 residents
Confidence Interval with % = (29.6%, 39.6%)
Confidence Interval with residents = (7400, 9900)
C. 24,475 to 24,525 residents
D. 23,250 to 25,750 residents