C883 Statistics and Probability for Secondary Mathematics Teaching
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Free C883 Statistics and Probability for Secondary Mathematics Teaching Questions
A uniform distribution over (0, 10) has mean:
- 5
- 0
- 10
- 2.5
Explanation
For a continuous uniform distribution over the interval (a, b), the mean is calculated as (a + b)/2. Substituting a = 0 and b = 10, the mean = (0 + 10)/2 = 5. Teaching this formula helps students calculate expected values for evenly distributed data.
Correct Answer:
5
A fair six-sided die is rolled. The probability of getting a number less than 3 is:
- 1/6
- 1/3
- 1/2
- 2/3
Explanation
A six-sided die has outcomes {1, 2, 3, 4, 5, 6}. The numbers less than 3 are 1 and 2, which are 2 favorable outcomes. Probability is calculated as the number of favorable outcomes divided by the total number of outcomes: 2/6 = 1/3. This shows that there is a one-third chance of rolling a number less than 3.
Correct Answer:
1/3
For teaching effect size, a Cohen’s d = 0.8 means:
- Large difference
- Moderate
- Small
- No difference
Explanation
Cohen’s d measures the standardized difference between two means. A value of 0.8 is considered a large effect size, indicating a substantial difference between groups relative to the variability in the data. Teaching this concept helps students interpret not only statistical significance but also practical significance in research results.
Correct Answer:
Large difference
A teacher conducts a survey using every 10th student on the roster. This is:
- Simple random
- Systematic
- Stratified
- Cluster
Explanation
Selecting every 10th student is an example of systematic sampling, where a fixed interval is used to select members from a population. This method is straightforward and ensures coverage across the roster, while differing from simple random sampling where each individual is chosen entirely at random.
Correct Answer:
Systematic
A stem-and-leaf plot preserves:
- Original data values
- Only summaries
- Shapes only
- Outliers hidden
Explanation
A stem-and-leaf plot organizes data so that the original values can still be retrieved. Each "stem" represents a group of values, while the "leaves" show individual data points within that group. This allows students to see both the distribution (shape) and the exact data values, making it a valuable tool for teaching data representation and analysis.
Correct Answer:
Original data values
Pie chart limitation for teaching:
- Hard to compare slices accurately
- Shows trends over time
- Handles negative values
- Best for continuous data
Explanation
Pie charts represent data as proportional slices of a circle. While they effectively show relative contributions of categories, it is difficult to compare slices accurately, especially when the differences are small. Pie charts do not display trends over time, cannot handle negative values, and are best suited for categorical rather than continuous data, which limits their instructional usefulness in some contexts.
Correct Answer:
Hard to compare slices accurately
In a scatterplot of study time vs test score, a positive trend suggests:
- Causation
- Correlation
- No relationship
- Negative association
Explanation
A positive trend in a scatterplot indicates that as one variable increases, the other variable tends to increase as well. This demonstrates a correlation, meaning there is a relationship between the variables. However, correlation does not imply causation; it simply shows that higher study time is associated with higher test scores, but it does not prove that studying more directly causes better scores.
Correct Answer:
Correlation
A teacher flips two coins. The sample space has how many equally likely outcomes?
- 2
- 3
- 4
- 6
Explanation
Flipping two coins results in all possible ordered outcomes: HH, HT, TH, TT. There are 4 equally likely outcomes, which form the sample space. Understanding sample space is essential for calculating probabilities and visualizing all possible events in a scenario.
Correct Answer:
4
For teaching confidence level, increasing from 95% to 99% will make the interval:
- Narrower
- Wider
- Unchanged
- Shift left
Explanation
Increasing the confidence level means we want to be more certain that the interval contains the true population parameter. To achieve higher confidence, the interval must cover more possible values, making it wider. This helps students understand the trade-off between confidence level and precision in confidence intervals.
Correct Answer:
Wider
A teacher uses a QQ-plot to check normality. Points fall along the line means:
- Data is skewed
- Data is approximately normal
- Outliers present
- Sample too small
Explanation
A QQ-plot compares observed quantiles with expected quantiles from a normal distribution. If the points fall approximately along the straight line, it indicates that the data is approximately normally distributed. Teaching QQ-plots helps students visually assess normality assumptions required for many statistical tests.
Correct Answer:
Data is approximately normal
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