Evaluating statistical claims: observational studies and experiments — Problem-Solving and Data Analysis

Questions in this quiz (10)

1. A researcher for a school district conducted a study to investigate the relationship between time spent using an online reading program and reading test scores. For the study, the researcher selected $$150$$ ninth-grade students at random from all ninth-grade students in the district. The table below shows the results for the $$120$$ students from the sample who used the program for at least $$1$$ hour per week.Which of the following is the largest population to which the findings of this study can be generalized?

   • All ninth-grade students in the district who scored $$80$$ or higher on the reading test
   • The $$150$$ students selected for the study
   • The $$120$$ students in the sample who used the program for at least $$1$$ hour per week
   • All ninth-grade students in the district

2. A high school principal wanted to assess the opinions of all students at the school about extending the school lunch period by $$15$$ minutes. The principal surveyed a sample of $$70$$ students who are members of the student council. The survey showed that the majority of those sampled supported extending the lunch period. Which of the following is true about the principal's survey?

   • The survey sample is biased because it is not representative of all students at the school.
   • The survey sample should have consisted only of students who do not participate in school activities.
   • The survey sample should have included only students who currently skip lunch.
   • It shows that the majority of students at the school support extending the lunch period.

3. To estimate the average number of hours students at a university spend studying per week, a researcher surveyed $$120$$ students who were studying in the university library on a Saturday evening. For the $$120$$ students surveyed, the average study time was $$12$$ hours per week. Which of the following statements is the most appropriate conclusion from this survey?

   • The average study time for all students at the university is $$12$$ hours per week.
   • A conclusion about the average study time of all students at the university should not be made because the sample size is too small.
   • The sampling method is flawed and may produce a biased estimate of the average study time of all students at the university.
   • The sampling method is not flawed and is likely to produce an unbiased estimate of the average study time of all students at the university.

4. An environmental scientist conducted an experiment to test the effect of a new irrigation method on the growth of tomato plants. For the experiment, the scientist selected a random sample of $$40$$ tomato farms from all tomato farms in a particular county. The scientist found that farms using the new irrigation method had a significant increase in tomato yield. What is the largest group to which the results of this study can be generalized?

   • The $$40$$ farms in the sample
   • All tomato farms in the county
   • All tomato farms in the state
   • All farms in the county

5. A researcher conducted a study about the use of digital textbooks in college courses. A group of $$80$$ instructors was randomly selected from all instructors at a university in City $$Z$$. Each instructor completed a survey, and $$52$$ reported that they regularly use digital textbooks in their classes. Which of the following is the broadest population to which the findings of this investigation can be generalized?

   • All college instructors in the country
   • All educators in City $$Z$$
   • All instructors at the university in City $$Z$$
   • All instructors in the sample

6. A researcher at an agricultural station in Kansas wanted to test the effect of a new soil treatment on the growth of a particular variety of soybean plants. From a large field of this soybean variety, the researcher randomly selected $$80$$ plants that were $$3$$ weeks old and randomly assigned them into two groups. Each group received a different soil treatment for $$6$$ weeks. At the end of the study, the average height of the plants in each group was measured and compared. Based on the design of this study, which of the following is the largest group to which the results can be generalized?

   • All $$80$$ soybean plants selected for the study
   • All soybean plants of this variety that were $$9$$ weeks old at the agricultural station
   • All soybean plants of this variety that were $$3$$ weeks old in Kansas
   • All soybean plants of this variety that were $$3$$ weeks old at the agricultural station

7. A beverage company conducted a survey to measure consumer interest in a new sparkling drink. The survey was posted on the company's official social media page, where followers could voluntarily respond. The results showed that $$82\%$$ of respondents preferred the new drink, while $$18\%$$ preferred the company's current drinks. Which of the following best explains why these results are unlikely to represent the preferences of the entire target market?

   • The percentages may change if more people respond to the survey.
   • Respondents to the survey were not randomly selected from the target market.
   • The survey compared only two types of drinks.
   • The survey did not include the total number of beverages sold by the company.

8. Suppose a company conducted a survey to assess customer satisfaction with a new mobile app. The table below displays the information for the customers in the sample.Which of the following is the largest population to which the results of this survey can be generalized?

   • All users who rated the app performance as Fast
   • The users in the sample
   • The users in the sample who rated the app performance as Fast
   • All users who have used the app

9. A university researcher conducted a study on the relationship between students' weekly exercise time and their grade point average. For the study, the researcher selected $$180$$ students at random from all students at a particular college. The table displays information for the $$130$$ students in the sample who reported exercising at least $$1$$ hour per week.Which of the following is the largest population to which the results of this study can be generalized?

   • The $$180$$ students selected for the study
   • The $$130$$ students who exercised at least $$1$$ hour per week
   • All students at the college who exercise more than $$3$$ hours per week
   • All students at the college

10. Near the end of a national radio talk show, the host invited listeners to respond to a poll on the show's website that asked, Do you support the new transportation policy discussed during the program. At the end of the show, the host reported that $$34\%$$ responded Yes and $$66\%$$ responded No. Which of the following best explains why the results are unlikely to represent the opinions of the entire population of the country?

    • The percentages should have been $$50\%$$ Yes and $$50\%$$ No.
    • The people who responded to the poll were not randomly selected from the population of the country.
    • The results should have included more response options besides Yes or No.
    • The show did not report how many total people listened to the program.