PSAT Math Multiple-Choice Practice Test 35: Data Analysis: Tables, Statistics, and Probability

1. In a local rock climbing group, the mean novice member age is 22 years and the mean experienced member age is 26 years. Which of the following can be concluded about the average age, a, of the experienced and novice members of this rock climbing group?

2. Data set K consists of the values 11, 4, 0, 7, 14, 1, 3, 7, and 13. Which of the following has the least value?

3. A polling company wanted to determine whether American voters would support a constitutional amendment that requires a person running for the U.S. Senate to have a minimum of a bachelor's degree. To do this, the company conducted a survey by sending 20,000 text messages across the entire United States to randomly selected phones with text-messaging capabilities. For every text that the company sent, it received a response to the survey. Which of the following best explains why this random sample is unlikely to be a representative sample of the American population's opinion in an actual election?

4. A medical testing company conducted an experimental study to determine which of three antihistamines is most effective for alleviating allergy symptoms. If the only allergies treated in the course of the study were pollen allergies, which of the following is true?

5. SoFast Internet is hoping to expand its services to three new counties in rural Virginia. According to its research, a total of approximately 86,400 homes in the three counties currently have Internet service. SoFast surveys a sample of 500 randomly selected households with Internet service and finds that 225 are not satisfied with their current provider. SoFast would be the only other Internet service provider in the area, and it is confident that it will be able to acquire 80% of the dissatisfied households. Based on this information and the results of the sample survey, about how many new customers should SoFast be able to acquire?

6. A psychology professor at a large university is conducting a research project on pre-law students' study habits for courses required for their majors versus their study habits for strictly elective courses. His original plan was to randomly select 250 third-year pre-law students and 250 fourth-year pre-law students and ask them to estimate the amount of time they spend studying for the two course types. Due to a printing error, only 200 survey copies were made; 50 of these went to third-years and 150 went to fourth-years. Assuming 100% of the surveys are returned, what effect(s) will the printing error have on the data collected?

Questions 7-8 refer to the following information.


The table above shows the number of apples, bananas, oranges, and pineapples sold at Freddie's Fruit Stand during each of the four seasons in 2018.

7. Of the following, which is closest to the percentage of all the pieces of fruit sold that were bananas?

8. For which season did pineapples make up the largest percentage of the total pieces of fruit sold?

9. Table 1

Age of Orange TreesPercent Distribution
Less than 3 years old15%
3–5 years old20%
6–10 years old25%
Older than 10 years40%

A large fruit orchard has 2,500 orange trees. Table 1 above shows the distribution of ages of the orange trees in the orchard. A county inspector has been notified that a highly contagious bacterial disease called citrus canker has infected some of the orange trees. The inspector randomly tests 4% of each age group of the trees. Her findings are shown in Table 2 below.

Table 2

Age of Orange TreesNumber with Citrus Cankers
Less than 3 years old8
3–5 years old6
6–10 years old8
Older than 10 years3

What is the probability that an orange tree selected at random from the tested trees less than 3 years old will have citrus canker?

Questions 10-11 refer to the following information.

The table below shows the distribution of applicants by age and level of education for a management trainee program offered at a retail store.

Age GroupHigh School Diploma Only2-Year Degree4-Year DegreeTotal
Older than 452204

10. According to the data, which age group had the smallest percentage of people with a high school diploma only?

11. Based on the table, if a single applicant is selected at random from all the applicants, what is the probability that he or she will have a 2-year degree and be at least 26 years old?

Questions 12-13 refer to the following information.

A team of researchers studied the effect of sleep masks on rapid eye movement (REM) sleep. Study participants were divided into three groups: the first group did not wear sleep masks, the second group wore regular sleep masks, and the third group wore sleep masks that were contoured away from the eyes and lashes. The results of the study are shown in the following table.

No MaskRegular MaskContoured MaskTotal
Experienced REM Sleep143378125
Did Not Experience REM Sleep34292285

12. What percent of the participants who experienced REM sleep during the study wore a contoured mask?

13. Based on the results of this study, if a company sold 12,000 of the contoured sleep masks, about how many of the consumers should experience REM sleep using the mask, assuming the participants in the study were a good representative sample?

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