PSAT Problem Solving and Data Analysis Practice (calculator)

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

• 300 randomly selected undergraduate students from all degree programs at the college

The first metacarpal bone is located in the wrist. The scatterplot 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

• 6

• 9

The first metacarpal bone is located in the wrist. The scatterplot 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

• 171 centimeters

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? (answer is a fraction)

A survey about voter participation in the 2012 US presidential election was conducted among a randomly chosen sample of US citizens. The table summarizes the results by age group.

According to the table, which age group has the greatest percentage of people who reported voting in the 2012 presidential election?

• 18–34

• 35–54

• 55–74

• 75 and older

A survey about voter participation in the 2012 US presidential election was conducted among a randomly chosen sample of US citizens. The table summarizes the results by age group.

A second sample of 50 people from the 18–34 age group who reported voting in the 2012 presidential election were selected at random and asked which candidate they voted for. Of these people, 29 responded that they voted for Candidate A, and 21 responded that they voted for someone else. Based on this information, which of the following is the most appropriate estimate of the number of people from the 18–34 age group in the survey who voted for Candidate A in the 2012 presidential election?

According to the table, which age group has the greatest percentage of people who reported voting in the 2012 presidential election?

• 1,247

• 771

• 365

• 176

At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?

• m = 17

• m > 17

• m < 17

• 15 < m < 19

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.

• 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 in 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 in exercise for 16-year-olds in the world.

The scatterplot shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

• 0.75

• 75

• 150

• 750

A researcher places two colonies of bacteria into two petri dishes that each have an area of 10 square centimeters. After the initial placement of the bacteria (t = 0) the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown above, where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the data above?

• At time t = 0, both dishes are 100% covered by bacteria.

• At time t = 0, bacteria covers 10% of Dish 1 and 20% of Dish 2

• At time t = 0, Dish 2 is covered with 50% more bacteria than Dish 1.

• For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.