Inference from sample statistics and margin of error — Problem-Solving and Data Analysis

Questions in this quiz (10)

1. A researcher surveyed $$1,000$$ randomly selected US residents about their views on the use of renewable energy sources. The table summarizes the responses.If the population of the United States was $$340,000,000$$ when the survey was conducted, based on the sample data of $$1,000$$ US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat or strongly support renewable energy and the number of those who somewhat or strongly oppose it? Round the answer to the nearest whole number.

   • $$61$$
   • $$65$$
   • $$72$$
   • $$76$$

2. A research group conducted a survey of a random sample of students at a certain high school to determine their preference for a new cafeteria menu. The high school has a total of $$4200$$ students. The survey showed that $$58\%$$ of the sampled students preferred the new menu. The margin of error for the survey was $$\pm4\%$$. Based on this information, which of the following is a plausible value for the total number of students at the high school who would prefer the new cafeteria menu?

   • $$2100$$
   • $$2436$$
   • $$2772$$
   • $$3024$$

3. A public health agency conducted a survey in a city with a population of $$24000$$ to estimate the prevalence of a certain allergy. A random sample of $$120$$ people from the city were tested, and $$18$$ people in the sample were found to have the allergy. Based on this sample, approximately how many people in the city would be expected to have the allergy?

   • $$3000$$
   • $$3200$$
   • $$3600$$
   • $$4000$$

4. A manufacturing company has $$600$$ employees. To estimate the average number of hours employees spend using computers per day, a researcher selected a random sample of $$100$$ employees and found that they used computers for an average of $$5.5$$ hours per day. The margin of error for this estimate is $$0.5$$ hours. Based on these results, which of the following is NOT a plausible value for the total number of hours employees use computers per day across all $$600$$ employees?

   • $$3000$$
   • $$3300$$
   • $$3600$$
   • $$4200$$

5. The results of two independent studies on the weekly study time of college students are shown below. The studies took random samples from the same large population, and the margins of error were calculated using an identical method.Which of the following is the most likely reason that the margin of error for study $$1$$ is greater than the margin of error for study $$2$$?

   • The standard deviation of the data in study $$1$$ was smaller.
   • The mean study time calculated in study $$1$$ was lower.
   • The sample size of study $$1$$ was larger.
   • The sample size of study $$1$$ was smaller.

6. In a study of sleep habits, $$900$$ randomly selected US adults were asked how many hours they sleep each night and whether they drink caffeine regularly. The data are summarized in the table below. Based on the data from the study, an estimate of the percent of US adults who sleep $$8$$ or more hours per night is $$32\%$$, and the associated margin of error is $$5\%$$.Which of the following is a correct statement based on the given margin of error?

   • Approximately $$5\%$$ of the adults in the study who sleep $$8$$ or more hours are incorrectly classified.
   • It is not possible that the percent of all US adults who sleep $$8$$ or more hours is less than $$27\%$$.
   • The percent of all US adults who sleep $$8$$ or more hours is exactly $$32\%$$.
   • It is doubtful that the percent of all US adults who sleep $$8$$ or more hours is $$40\%$$.

7. A quality control inspector at a factory examined a random sample of $$200$$ batteries from a recent production run and found that $$6\%$$ of the batteries were defective. The factory produces battery packs in runs of $$200$$ units. If the factory completed $$3000$$ production runs in a month, which of the following is the best estimate of the number of batteries produced that month that are NOT defective?

   • $$36,000$$
   • $$564,000$$
   • $$600,000$$
   • $$636,000$$

8. The table shows the results of a survey conducted among $$80$$ randomly selected shoppers at a grocery store. They were asked which of two snack brands, $$X$$ or $$Y$$, they prefer buying.According to the survey, if $$240$$ consumers buy one of these two brands, by approximately how many purchases would Brand $$X$$ be expected to outnumber Brand $$Y$$?

   • $$16$$
   • $$24$$
   • $$48$$
   • $$72$$

9. Two portfolios received initial investments as indicated in the table.Portfolio $$A$$ grows at a $$4\%$$ annual rate compounded yearly, while Portfolio $$B$$ increases by a constant $$60$$ each year. Which of the following statements accurately compares the annual returns from Portfolio $$A$$ and Portfolio $$B$$ over a $$5$$-year period?

   • Portfolio $$A$$ consistently provides a higher annual return than Portfolio $$B$$.
   • Portfolio $$A$$ consistently provides a lower annual return than Portfolio $$B$$.
   • Initially, Portfolio $$A$$ provides a higher annual return than Portfolio $$B$$, but this trend reverses over time.
   • Initially, Portfolio $$A$$ provides a lower annual return than Portfolio $$B$$, but it eventually provides a higher return.

10. In a survey of $$750$$ randomly selected teenagers in the United States, students were asked about their frequency of watching online videos and their social media usage. The table summarizes the responses.According to the survey results, an estimated $$38\%$$ of US teens are classified as moderate social media users, with a margin of error of $$2\%$$. Which of the following statements is correct, considering the given margin of error?

    • The percentage of all US teens who are moderate social media users is exactly $$38\%$$.
    • It is improbable that the percentage of all US teens who are moderate social media users is $$45\%$$.
    • It is impossible for the percentage of all US teens who are moderate social media users to be $$36\%$$.
    • Exactly $$2\%$$ of the teenagers surveyed who are categorized as moderate social media users may not actually belong in that category.