a) A botanist at a nursery wants to inspect the health of the plants at the nursery. Which of the following best describes a systematic sample of plants? The botanist takes a list of the plants and selects every 3" plant until 78 plants are selected. The botanist forms groups of 13 plants based on the heights of the plants. Then, he randomly chooses 6 groups and selects all of the plants in these groups. All of the plants that are in one particular room at the nursery are easily accessible. So, the botanist selects the 78 plants in this particular room. (b) The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a random sample of attendees? The organizers select the first 60 attendees who register for the conference because these attendees are easily accessible. The organizers take a list of the attendees and select every 6" attendee until 60 attendees are selected. The organizers assign each attendee a different number. Using a random number table, the organizers draw 60 of those numbers at random. Then, the organizers select the attendees assigned to the drawn numbers. Every set of 60 attendees is equally likely to be drawn using the random number table. (c) Counselors at a college want to poll students about how much time the students spend studying. Which of the following best describes a cluster sample of students? The counselors use a computer program to draw 64 students at random and select these students. Every set of 64 students is equally likely to be drawn by the computer program. The counselors form groups of 8 students based on the students' majors. Then, the counselors select all of the students in 8 randomly chosen groups. The counselors form 4 groups of students based on the numbers of classes the students are taking. Then, the counselors select 16 students at random from each group.

A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.   Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other? Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective…

A large group of people get together. Each one rolls a die 120 times, and counts the number of aces (with a single dot). About what percentage of these people should get counts in the range 10 to 30? Choose the closest answer.

How many different ways are there to select a group of 4 out of 8 people for a survey?