AP Statistics Experimental Design and Random Assignment Worksheet Solutions (PDF)

(a) No treatments are imposed: observational. (b) Treatments are assigned: experiment. (c) Runners chose their shoes: observational.

(a) observational; (b) experiment; (c) observational.

Units: the 60 students. Explanatory variable: study method. Treatments: flash cards, video lesson, no special method (control). Response: quiz score.

60 students; method of studying; 3 treatments; quiz score.

Students who choose to take a course may be more motivated or have more resources.

Motivation (or family resources) is confounded with the course: it is associated with taking the course and also affects scores, so we cannot attribute the 80 points to the course.

The inactive pill is a placebo (control group).

Placebo control; double-blind. Blinding prevents expectations from influencing reported or rated pain.

05 selected, 41 skipped (out of range), 12 selected, 07 selected, 98 skipped (out of range), 03 selected, 12 skipped (repeat), 11 selected, 77 skipped (out of range), 09 selected.

Fertilizer group: plants 03, 05, 07, 09, 11, 12. The other six plants are the control group.

Randomly assign 20 students to 8 hours and 20 to 5 hours (for example by drawing names), have every group do the same memory test the next day, and compare the mean scores.

Random assignment of 20 students per group, same test for all, compare the group means.

Experience strongly affects running time. Blocking compares the shoes within similar runners.

Blocking removes the variation due to experience, making any shoe effect easier to see.

Each student receives both treatments.

Matched pairs design (each student is their own control); it removes person-to-person differences in typing speed.

One cake per oven gives no information about the usual variation.

She needs replication: bake many cakes in each oven, randomly assigned.

Random selection supports generalizing to the city. Random assignment supports cause and effect.

They can generalize to all adults in the city and conclude that the difference in results was caused by the diets.

Volunteers are not a random sample.

Cause and effect: yes (random assignment). Generalization to all teenagers: no (volunteers).

A 2% chance is small.

The result is statistically significant: a difference of 6 points is unlikely if tutoring had no effect, so there is evidence tutoring helps.

Volunteering and class period are not random.

Groups were not formed by random assignment (volunteers differ), and the class period is confounded with the treatment.

Randomly assign 25 volunteers to the energy drink and 25 to a look-alike placebo drink. A third person prepares the cups, so neither the volunteers nor the tester knows who got which. Compare mean reaction times.

Random assignment, placebo, double-blind, same test for both groups, compare the means.

Plants grow even without fertilizer.

A control group provides a baseline, so any difference can be attributed to the fertilizer.

Coffee drinkers may differ in income, exercise, or health.

Confounding variables (such as lifestyle or income) could explain the longer life, so causation cannot be concluded.

Blocks: sprinters and distance runners.

Randomly assign 6 sprinters to plan 1 and 6 to plan 2; do the same for the distance runners. Compare the plans within each block.

\(\frac{60}{3}=20\) seeds per condition.

20 seeds per condition. Number the seeds 01 to 60, select 20 labels for condition 1, then 20 more for condition 2; the rest go to condition 3.

Was there a comparison group, and was assignment random?

There is no control group and no random assignment, so we do not know what would have happened without the pill. Blinding is also not mentioned.

A: \(\frac{27}{45}=60\%\). B: \(\frac{36}{45}=80\%\). Difference: 20 percentage points.

B improved at 80% compared with 60% for A. We need to know how likely a 20-point difference is by chance (a significance test) to call it statistically significant.