Review AP Statistics Unit 1 by framing studies, classifying variables, representing and comparing distributions, and evaluating sampling and experimental design.
A trainer has two weight lifting classes, Class I and Class II. Each class has 9 amateur adult males and 1 professional adult male. Their body weights and number of bench press reps with 225 pounds are shown in the following dotplots. The professionals are designated as A and B.
Identify the type of study.
Identify and classify the quantitative variables.
Determine the population for a valid investigative question.
An environmental research agency conducted a study of a certain state's roadsides to estimate the mean number
of discarded cans and bottles per mile of public road. The state's public roads were grouped into three types:
Major highways: major paved roads designed for high traffic volume
Minor highways: smaller paved roads designed for low traffic volume
Unpaved roads: gravel and dirt roads
There are about 100,000 miles of public roads in the state. The environmental research agency defined a
sampling unit to be a one-mile segment of public road. Using a database supplied by the state's department of
transportation, the agency randomly selected 30 one-mile road segments for each of the three types of roads.
Researchers from the agency searched the roadsides along each of the selected one-mile road segments and
recorded the number of discarded cans and bottles. Results are shown in the table below.
What is the variable of interest in the study?
What is the parameter of interest?
Were the data in the study obtained by a simple random sample, a stratified random sample, or a cluster
sample? Explain.
A horticulturist plans a study on the use of compost tea for plant disease management. She obtains 18 identical beds, each containing a random selection of five minipink rose plants. Some bed or beds will not receive compost tea. For those beds receiving compost tea, she plans to use two different composting times (2 and 5 days), two different compost preparations (aerobic and anaerobic), and two different spraying techniques (with and without adjuvants). Midway into the growing season she will check all plants for rose powdery mildew disease.
Identify the experimental units.
Identify the treatments.
Explain why the horticulturist included a group that does not receive compost tea.
Explain the advantage of using only minipink roses in this study.
Explain a disadvantage of using only minipink roses in this study.
Using the proportion of plants in each bed that are infected, identify an appropriate graphical representation.
Explain why a histogram would not be appropriate.
Determine a valid investigative question about infection proportions in beds using aerobic and anaerobic preparations.
Tropical storms in the Pacific Ocean with sustained winds that exceed 74 miles per hour are called typhoons. Graph A below displays the number of recorded typhoons in two regions of the Pacific Ocean-the Eastern Pacific and the Western Pacific-for the years from 1997 to 2010.
GRAPH A
Compare the distributions of yearly frequencies of typhoons for the two regions of the Pacific Ocean for the years from 1997 to 2010.
For each region, describe how the yearly frequencies changed over the time period from 1997 to 2010.
A moving average for data collected at regular time increments is the average of data values for two or more consecutive increments. The 4 -year moving averages for the typhoon data are provided in the table below. For example, the Eastern Pacific 4-year moving average for 2000 is the average of 22, 16, 15, and 21, which is equal to 18.50.
Show how to calculate the 4-year moving average for the year 2010 in the Western Pacific. Write your value in the appropriate place in the table.
Graph B below shows both yearly frequencies (connected by dashed lines) and the respective 4-year moving averages (connected by solid lines). Use your answer in part (c) to complete the graph.
GRAPH B
Consider graph B.
What information is more apparent from the plots of the 4-year moving averages than from the plots of the yearly frequencies of typhoons?
What information is less apparent from the plots of the 4-year moving averages than from the plots of the yearly frequencies of typhoons?