Quantitative Data in Economics Quiz

A correlation coefficient of −0.85 indicates a strong negative relationship between the two variables. This means that as one variable increases, the other tends to decrease significantly. The value close to -1 reflects a strong inverse association, suggesting that the variables are closely related in opposing directions.

As the sample size increases, the standard error of the mean decreases because larger samples provide more accurate estimates of the population mean. This reduction in variability occurs because the sample mean becomes a more stable and reliable measure, reflecting less fluctuation due to random sampling errors.

A confidence interval provides an estimated range within which a population parameter is likely to fall, based on sample data. It includes a specified probability, indicating the level of confidence that the interval contains the true parameter value, rather than guaranteeing it, which distinguishes it from definitive statements about exact values.

Stratified sampling involves dividing the population into distinct subgroups or strata based on specific characteristics. This method ensures that each subgroup is represented proportionately in the sample, allowing for more accurate and reliable results. By randomly selecting individuals from each group, it captures the diversity within the population effectively.

In a normal distribution, about 68% of the data falls within one standard deviation of the mean. This characteristic illustrates the concentration of values around the mean, indicating that most observations lie close to the average, thus reflecting the distribution's symmetrical nature.

A line graph is ideal for displaying changes over time, such as GDP fluctuations over 20 years. It effectively illustrates trends and allows for easy comparison of values across different time points, highlighting increases or decreases in GDP. Other visualizations like pie charts or bar charts are less effective for this purpose.

Causation cannot be definitively established based solely on a correlation coefficient because correlation only indicates a relationship between two variables, not the nature of that relationship. Other factors, such as confounding variables or coincidence, may influence the correlation, making it essential to conduct further analysis to determine causation.

The mean is calculated by adding all values and dividing by the number of values, making it sensitive to extreme values (outliers). A single very high or low value can significantly skew the mean, whereas the median and mode remain unaffected by such outliers, providing a more stable measure of central tendency in skewed distributions.

A p-value of 0.03 suggests there is a 3% probability of observing the data if the null hypothesis is true, but it does not prove that the null hypothesis is false. Statistical significance does not equate to certainty; it only indicates evidence against the null hypothesis. Thus, it is incorrect to claim it is definitely false.

In this scenario, the independent variable is the factor that is manipulated to observe its effect on another variable. Here, raising the minimum wage is the variable being tested for its impact on employment levels, making it the independent variable that influences the outcome.

This scenario illustrates primary data collection, as the economist gathers original price information directly from households. Unlike secondary data, which involves analyzing existing data, primary data is specifically collected for the research purpose at hand, ensuring its relevance and accuracy for the study.

An R² value of 0.72 indicates that 72% of the variance in the dependent variable is accounted for by the regression model. This suggests a strong relationship between the independent variables and the dependent variable, as a higher R² value indicates better explanatory power of the model.