Command of Evidence (Quantitative) Flashcards

A researcher studies the relationship between hours of sleep and test scores. The scatter plot shows a correlation coefficient of r = 0.73. Which statement best describes this relationship?

Answer: There is a strong positive correlation between sleep and test scores

A correlation coefficient of r = 0.73 indicates a strong positive correlation (closer to 1.0), meaning as hours of sleep increase, test scores tend to increase significantly.

A survey of 500 students shows that 60% prefer online learning. The margin of error is ±4%. Which conclusion is most appropriate?

Answer: Between 56% and 64% of all students likely prefer online learning

The margin of error of ±4% means the true population proportion likely falls between 60% - 4% = 56% and 60% + 4% = 64%.

Which of the following scenarios would most likely produce a biased sample when studying average income in a city?

Answer: Surveying people at luxury shopping malls only

Surveying only at luxury shopping malls would create selection bias by overrepresenting higher-income individuals, making the sample unrepresentative of the city's population.

A study finds that students who eat breakfast score 15 points higher on average than those who don't. What additional information is most needed to evaluate this finding?

Answer: The standard deviation of the scores and sample sizes

Standard deviation and sample sizes are crucial for determining if the 15-point difference is statistically significant or could be due to random variation.

A line of best fit for data comparing study time (x) and test scores (y) has the equation y = 2.5x + 65. What does the y-intercept represent in this context?

Answer: The predicted test score for a student who studies 0 hours

The y-intercept (65) represents the predicted value of y when x = 0, which in this context means the predicted test score when study time is 0 hours.

Two groups of 100 students each take different versions of a test. Group A has a mean of 78 with standard deviation 12. Group B has a mean of 82 with standard deviation 8. Which statement is most accurate?

Answer: Group B performed better and more consistently than Group A

Group B has a higher mean (82 vs 78) indicating better performance, and a lower standard deviation (8 vs 12) indicating more consistent scores with less variability.