Math Questions Calculator Permitted Exam 1 — Questions and Answers
Question 1: A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology-degree program read per day?
- 40 randomly selected undergraduate psychology-degree program students
- 40 randomly selected undergraduate students from all degree programs at the college
- 300 randomly selected undergraduate psychology-degree program students (Correct answer)
- 300 randomly selected undergraduate students from all degree programs at the college
Correct answer: 300 randomly selected undergraduate psychology-degree program students
A smaller margin of error in a survey estimate is achieved by increasing the sample size, as larger samples provide more precise estimates. Additionally, the sample must be drawn from the specific population of interest to ensure the results are generalizable. Therefore, selecting 300 students from the psychology-degree program (a larger sample from the target population) will most likely result in a smaller margin of error compared to a smaller sample or a sample from a different population.
Question 2: The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
- 2
- 4 (Correct answer)
- 6
- 9
Correct answer: 4
To find how many people's actual height differs by more than 3 cm from the predicted height, you need to visually inspect the scatterplot. For each data point, estimate its actual height (y-coordinate) and the predicted height (y-value on the line of best fit for that x-coordinate). Count the points where the vertical distance between the actual point and the line of best fit is greater than 3 centimeters.
Question 3: The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?
- The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone (Correct answer)
- The predicted first metacarpal bone increase in centimeters for every centimeter increase in height
- The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters
- The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters
Correct answer: The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone
The slope of a line of best fit represents the average change in the dependent variable (y-axis) for every one-unit increase in the independent variable (x-axis). In this context, height is the dependent variable and metacarpal bone length is the independent variable. Therefore, the slope indicates the predicted increase in height (in centimeters) for each one-centimeter increase in the first metacarpal bone length.
Question 4: The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?
- 168 centimeters
- 169 centimeters
- 170 centimeters (Correct answer)
- 171 centimeters
Correct answer: 170 centimeters
To find the predicted height for a metacarpal bone length of 4.45 centimeters, locate 4.45 on the x-axis (metacarpal bone length). Then, move vertically up from 4.45 until you intersect the line of best fit. From that intersection point, move horizontally to the left to read the corresponding value on the y-axis (height), which will be approximately 170 centimeters.
Question 5: A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?
- One
- Two (Correct answer)
- Three
- Four
Correct answer: Two
The solutions to a system of equations are the points where all of their graphs intersect simultaneously. By examining the provided graph, identify the points where all three lines or curves cross each other. In this case, there are two distinct points where all three graphs converge, indicating two solutions to the system.
Question 6: The table below classifies 103 elements as metal, metalloid, or nonmetal and as solid, liquid, or gas at standard temperature and pressure. What fraction of all solids and liquids in the table are metalloids?
- 7 over 92. (Correct answer)
- 2 over 90
- 90 over 103
- 7 over 103
Correct answer: 7 over 92.
To find the fraction, first identify the total number of solids and liquids by summing the 'Solid' and 'Liquid' rows across all categories (Metal, Metalloid, Nonmetal). Then, find the number of metalloids that are either solid or liquid. The fraction is the number of solid/liquid metalloids divided by the total number of solids and liquids.
Question 7: A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results. According to the table, for which age group did the greatest percentage of people report that they had voted?
- 18- to 34-year-olds
- 35- to 54-year-olds
- 55- to 74-year-olds (Correct answer)
- People 75 years old and over
Correct answer: 55- to 74-year-olds
To determine which age group had the greatest percentage of people report voting, you need to calculate the percentage for each group. For each age group, divide the number of people who reported voting by the total number of people in that age group, then multiply by 100. Compare these percentages to identify the highest one, which corresponds to the 55- to 74-year-olds.
Question 8: A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results. A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results.
- About 123 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
- About 76 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
- About 36 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
- About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election. (Correct answer)
Correct answer: About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
To estimate the number of 18-34 year olds who voted for Candidate A, you need two pieces of information from the survey table: the percentage of 18-34 year olds who reported voting, and the percentage of those voters who voted for Candidate A. Multiply these percentages by the total population of 18-34 year olds (which would be provided in the full context of the problem, likely around 46 million) to get the estimated number of voters for Candidate A in that age group.
Question 9: A researcher wanted to know if there is an association between exercise and sleep for the population of 16-year-olds in the United States. She obtained survey responses from a random sample of 2000 United States 16-year-olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?
- There is a positive association between exercise and sleep for 16-year-olds in the United States. (Correct answer)
- There is a positive association between exercise and sleep for 16-year-olds in the world.
- Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16-year-olds in the United States.
- Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16-year-olds in the world.
Correct answer: There is a positive association between exercise and sleep for 16-year-olds in the United States.
Because the researcher used a random sample of 16-year-olds *in the United States*, the findings can be generalized to the entire population of 16-year-olds in the United States. However, the study only found an 'association,' not causation, and it cannot be generalized to 16-year-olds worldwide. Therefore, the conclusion that there is a positive association between exercise and sleep for 16-year-olds in the United States is well supported.
Math Questions Calculator Permitted Exam 1
A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university.
She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes.
Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error.
Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology-degree program read per day?