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Statistical study and data interpretation
This test develops planning of a statistical investigation and justified interpretation of data. Tasks cover populations, samples, variable types, the mean, standard deviation, outliers and the reliability of conclusions.
Questions: 10Estimated time: 21 minutes
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Question 1out of 10
What type of variable is precisely measured human height?
The population is the full group studied and the sample is the observed subset. Precisely measured height is a quantitative continuous variable. Research proceeds through question, collection, analysis, interpretation and conclusion. An outlier can strongly affect the mean, standard deviation and regression line.
Question 2out of 10
What is a logical sequence of stages in a statistical study?
The population is the full group studied and the sample is the observed subset. Precisely measured height is a quantitative continuous variable. Research proceeds through question, collection, analysis, interpretation and conclusion. An outlier can strongly affect the mean, standard deviation and regression line.
Question 3out of 10
Model A has R² = 0.60. After adding another predictor, model B has R² = 0.76. By what percentage did the part of variation unexplained by model A decrease?
First find the variation unexplained by model A: 1 − R²(A). Then find its decrease: R²(B) − R²(A). The relative decrease is (R²(B) − R²(A)) / (1 − R²(A)) · 100%. Do not confuse percent with percentage points.
Question 4out of 10
In one class, 14 students achieved an average score of 16. In another class, 14 students achieved an average score of 10. What is the average score of all students in both classes combined?
Do not simply add the two means and divide by 2 because the groups have different sizes. Find each group total by multiplying its mean by its number of students. Add the two totals and divide by the total number of students: (n₁m₁ + n₂m₂) / (n₁ + n₂).
Question 5out of 10
Model A has R² = 0.40. After adding another predictor, model B has R² = 0.52. By what percentage did the part of variation unexplained by model A decrease?
First find the variation unexplained by model A: 1 − R²(A). Then find its decrease: R²(B) − R²(A). The relative decrease is (R²(B) − R²(A)) / (1 − R²(A)) · 100%. Do not confuse percent with percentage points.
Question 6out of 10
In one class, 15 students achieved an average score of 6. In another class, 15 students achieved an average score of 16. What is the average score of all students in both classes combined?
Do not simply add the two means and divide by 2 because the groups have different sizes. Find each group total by multiplying its mean by its number of students. Add the two totals and divide by the total number of students: (n₁m₁ + n₂m₂) / (n₁ + n₂).
Question 7out of 10
How can an outlier affect statistical analysis?
The population is the full group studied and the sample is the observed subset. Precisely measured height is a quantitative continuous variable. Research proceeds through question, collection, analysis, interpretation and conclusion. An outlier can strongly affect the mean, standard deviation and regression line.
Question 8out of 10
The standard deviation of variable X is 3. A new variable is defined as Y = 2X + 8. What is the variance of Y?
Adding the constant b does not change variance. Multiplying every value by k multiplies the standard deviation by |k| and the variance by k². Therefore Var(Y) = (k · s)².
Question 9out of 10
Some school students were surveyed. What are the surveyed group and all school students called?
The population is the full group studied and the sample is the observed subset. Precisely measured height is a quantitative continuous variable. Research proceeds through question, collection, analysis, interpretation and conclusion. An outlier can strongly affect the mean, standard deviation and regression line.
Question 10out of 10
What conclusion about causation does correlation permit?
The dependent variable is the response predicted by the model. Assess fit using R², residual patterns, context and prediction range. Correlation alone does not prove causation; a third factor may explain it.
Time left: 00:00:00
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Sample questions
- Calculate the combined mean of two groups of different sizes.
- The standard deviation of variable X is s. A new variable is defined as Y = kX + b. What is the variance of Y?
- Some school students were surveyed. What are the surveyed group and all school students called?
- What type of variable is precisely measured human height?
- Compare the R² values of two models and calculate by what percentage the first model's unexplained variation decreased.
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