1. The histogram shown summarizes the responses of 100 people when asked, “What was the price of the last meal you purchased?”
Based on the histogram, which of the following could be the interquartile range of the prices?
2. Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?
(A) Negative 1Negative 1 Negative 1
(B) Negative 0 point 7 5 Negative 0 point 7 5 Negative 0 point 7 5
3. A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table.
Based on the data in the table, which of the following is the most appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification?
(A) Back-to-back stemplots
(C) Side-by-side boxplots
(D) Segmented bar chart
4. A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample?
(A) Select all female students on the list.
(B) Randomly select 50 students on the list.
(C) Randomize the names on the list and then select every tenth student on the randomized list.
(D) Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.
(E) Randomly select 50 students on the list who are attending college.
1. The students enrolled in honors biology at a high school were given the task of using a spreadsheet program to investigate a topic in genetics. All students in the class had similar background knowledge of the topic. Some students in the class had no spreadsheet experience, Group R, and needed time to learn the program to complete the task. The rest of the students, Group S, had previous spreadsheet experience and typically took less time to complete the task. Each of the histograms below show the distribution of completion times, in minutes, for one of the two groups.
(a) Of the two histograms shown, I and II, which is more likely to be the distribution of completion times for the students in Group R? Justify your answer.
(b) Describe the shape of a histogram created from the data of the two groups of students combined.
(c) Consider the population of all students in honors biology classes in the high school’s state who are given the task of using the spreadsheet program to investigate the topic in genetics. The distribution of the completion times has a shape similar to the combined histogram of students at the high school, with mean 70 minutes and standard deviation 26.5 minutes. For random samples of 50 students taken from the population, describe the sampling distribution of the sample mean completion time.
2. Researchers are designing an experiment to compare two different types of running shoes, A and B, to investigate which type is better for minimizing running time for a one-mile run. The experiment will consist of distributing the shoes to runners who are classified as either professional or recreational. A randomized block design is planned, with blocking by classification of runner. Random samples of 50 professional runners and 50 recreational runners will be selected. Each runner within each classification will be randomly assigned to wear either the type A shoe or the type B shoe, and their running times will be recorded for a one-mile run.
(a) What is a statistical advantage of blocking by the classification of runner?
(b) Why is it important to randomize the type of shoe the runner will wear instead of allowing the runner to choose the shoe?
(c) Explain how the design of the experiment will address replication. What is the benefit of the replication?