Poll and Concrete Strength Analysis Quiz

A cable news show displays the results of a poll for a two-candidate runoff election between candidate A and candidate B. The poll shows that candidate A is leading with 53% of the vote. In small print at the bottom of the graphic, it says ±4.9%. Which of these statements is true about this poll?

• Candidate A will win because the mean percentage for the poll is greater than 50.

• Candidate A cannot get more than 58% of the vote.

• The poll predicts that between 48.1% and 57.9% of voters will select candidate A in the election.

• The poll should not be trusted since it has a margin of error attached to it.

In the 1940s, the U.S. Department of Commerce reported a new way to test the tensile strength, in pounds per square inch, of concrete. Several samples of concrete specimens were used to estimate the mean tensile strength of 430 pounds per square inch with a margin of error of 10 pounds per square inch. After the study was published, another group proposes to run the same test on concrete specimens but with samples including many more concrete specimens in each sample. Which of these statements is most likely to be true about the second study?

• The estimated mean will be greater than 440 pounds per square inch.

• The margin of error for the second study will likely be around 10 pounds per square inch.

• The margin of error for the second study will likely be greater than 10 pounds per square inch.

• The margin of error for the second study will likely be less than 10 pounds per square inch.

Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram. Which of these conclusions and justifications is the most reasonable?

• A. The difference in means for the two treatment groups is likely due to the random assignment since the difference is negative.

• B. The difference in means for the two treatment groups is likely due to the random assignment since there is at least one value in the histogram with a greater absolute difference than 11.47 gallons of gas.

• C. The randomization distribution does not give any evidence that the difference between the two treatment groups is due to the special instructions.

• D. The randomization distribution provides strong evidence that the difference in means for the two treatment groups is due to the treatment because the difference is highly unlikely based on random assignment alone.

A student measures the wingspans of 40 local dragonfly specimens selected at random. The sample mean is 6.8 centimeters with a margin of error of 0.9 centimeters. Based on this information, what are plausible values for the mean wingspans of the population of local dragonflies?

• A. between 6 cm and 7 cm

• B. 6.8 cm

• C. between -5.7 cm and 10 cm

• D. between 5.7 cm and 7.7 cm

Which of the following best describes the difference between an observational study and an experiment?

• Observational studies always have larger sample sizes

• Experiments involve manipulating variables while observational studies do not

• Observational studies are always more accurate

• Experiments never have control groups

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

• 95%

• 99.7%

• 68%

• 50%

What is the primary purpose of randomization in statistical studies?

• To make the study easier to conduct

• To reduce the impact of confounding variables

• To increase the sample size

• To eliminate the need for control groups

A z-score of -2 indicates that a data point is:

• At the mean

• Two standard deviations below the mean

• Two standard deviations above the mean

• At the median

Which type of data would be considered secondary data?

• Interviews you conduct personally

• Data collected from government census records

• Surveys you distribute to participants

• Direct observations you make

When evaluating a statistical study, what is the most important consideration regarding ethics?

• The sample size used

• The statistical methods employed

• The protection of participant privacy and consent

• The cost of the study