18A/B

425 469 300 490 415 285 507 336 503 442
307 317 251 397 294 263 406 262 391 356
Observation Car model kWh/100 miles
1 Porsche Taycan 4S Cross Turismo 45
2 Volkswagen ID.4 Pro S 35
3 Hyundai Kona Electric 27
4 Ford Mustang Mach-E RWD 34
5 Tesla Model S Performance 35
6 Tesla Model X Performance 35
7 Nissan Leaf SV/SL 32
8 Tesla Model S Plaid 33
9 Volkswagen ID.4 Pro 34
10 BMW i3s 30
Random number kWh/100 miles
Random number kWh/100 miles
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Understand how fuel efficiency is measured for electric cars. 1
Use technology to generate random numbers. 2
Select a bootstrap sample and calculate its mean. 2

Two people putting things in the back of a car A dotplot labeled “kWh/100 Miles Rating” and numbered in increments of 5 from 25 to 45. There is a dot at approximately 27, a dot at approximately 30, a dot at approximately 32, a dot at approximately 33, two dots at approximately 34, three dots at approximately 35, and a dot at approximately 45. A selection menu. At the top, “The Bootstrap For One Sample” is selected while “Build Sampling Distribution” and “Get Confidence Interval” are unselected. Beneath these is a heading reading “Enter Data,” under which “Your Own” has been selected from a dropdown. To the right of this is text that reads “Enter observations or copy & paste from spreadsheet.” Beneath the dropdown is another heading reading “Name of Variable” and “kWh/100 Miles Rating” has been input in the space below. The next heading says “Enter observations (separated by space or comma)” and in the input box below, it reads “45, 35, 27, 34, 35, 35, 32, 33, 34, 30.” The next heading reads “Select Plot Type” and “Dotplot” has been selected beneath it, while “Histogram” and “Adjust Size of Dots” are unselected. Under this is a line and then another heading, reading “Statistic of Interest,” which has “Mean” selected from a dropdown beneath. Under that is a heading reading “Select how many bootstrap samples you want to generate” and 1 has been selected. Underneath this is a button labeled “Draw Bootstrap Sample(s)” and another button labeled “Reset.” Some tables and graphs. The first table is titled “Summary Statistics For Bootstrap Distribution.” The columns are “Bootstrap Samples,” “Statistic,” “Unique Values,” “Mean,” “Standard Deviation,” “Min,” “Q1,” “Median,” “Q3,” and “Max.” The values are 1,000, Mean, 605, 417, 24.4, 346, 400, 419, 434, and 481. Beneath this table is a graph titled “Bootstrap Sampling Distribution” and labeled “Sample Mean x bar” on the x-axis and “Frequency” on the y-axis. The graph has a peak at approximately 420. There is a label reading “2.5th Percentile” at approximately 365, another label reading “Observed Mean” at approximately 420, and another label reading “97.5th Percentile” at approximately 465. Beneath this graph is another graph titled “95% Bootstrap Confidence Interval” and labeled “Population Mean (C02 Emission Rating)” on the x-axis. It has a point at approximately 415 with a range labeled as “[367, 463].” Beneath this is another table, this one titled “Bootstrap Percentile Confidence Interval.” It has columns “Population Parameter,” “Point Estimate,” “Lower Bound,” “Upper Bound,” and “Confidence Level.” The values are “Mean,” 417, 367, 463, and 95%. A selection menu. At the top, “Generate Random Numbers” has been selected, while “Random Numbers” and “Coin Flips” are unselected. There is a heading reading “Choose Minimum,” under which “1” has been input, and to the right, there is a heading reading “Choose Maximum,” under which “10” has been input. Beneath these is another heading reading “How many numbers do you want to generate?” with “10” input beneath it. To the right is another heading reading “Sample with Replacement?” and there are selection options for “No” and “Yes,” where “yes” has been selected. Beneath these is two buttons, one reading “Generate” and the other reading “Reset.”

0.1 0.4 0.6 0.8 1.3 1.5 1.6 1.7
1.8 1.8 1.9 1.9 1.9 2.0 2.2
0.1 0.4 0.6 0.8 1.3 1.5 1.6 1.7
1.8 1.8 1.9 1.9 1.9 2.0 2.2
Petting 114 203 217 254 256 284 296
Vocal praise 4 7 24 25 48 71 294
0.1 0.4 0.6 0.8 1.3 1.5 1.6 1.7
1.8 1.8 1.9 1.9 1.9 2.0 2.2
Petting 114 203 217 254 256 284 296
Vocal praise 4 7 24 25 48 71 294
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Create a bootstrap confidence interval for a population median. 1
Determine when it is appropriate to use a two-sample t confidence interval to estimate a difference in means. 2

A dotplot titled “Jump Distance (meters).” There is a dot at 0.1, another at 0.4, another at 0.6, another at 0.8, another at 1.2, another at 1.5, another at 1.6, another at 1.7, two at 1.8, three at 1.9, another one at 2.0, and one more at 2.2.

Descriptive Statistics:

Group Sample Size Mean Std. Dev. Min Q1 Median Q3 Max
Petting 7 232.0 61.7 114 210.0 254 270 296
Vocal Praise 7 67.6 102.5 4 15.5 25 59.5 294

Two side-by-side dot plots labeled “Time (in seconds)” on the x-axis. The first plot is labeled “Petting” and has a point at approximately 115, another at approximately 205, another at approximately 215, two at approximately 255, another at approximately 285, and another at approximately 295. The second plot is labeled “Vocal Praise” and has two dots at approximately 5, two at approximately 25, one at approximately 50, another at approximately 70, and another at approximately 295.

Glossary 18A

sampling without replacement
sampling where once an individual from the population is selected for the sample and data are recorded for that individual, they are not considered again when making additional selections from the population for that sample.
sampling with replacement
sampling where after an individual is selected for the sample and data are recorded for that individual, they are “replaced” (put back into the population) before the next selection is made.
bootstrap sample
a sample that is selected from the values in the original sample.