C883 Statistics and Probability for Secondary Mathematics Teaching
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Free C883 Statistics and Probability for Secondary Mathematics Teaching Questions
The null hypothesis for testing if a new teaching method improves scores is usually:
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μ_new > μ_old
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μ_new = μ_old
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μ_new ≠ μ_old
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μ_new
Explanation
The null hypothesis (H₀) typically states that there is no effect or difference—in this case, that the new teaching method does not change the mean score compared to the old method. Therefore, H₀: μ_new = μ_old. This sets up a framework for testing whether observed differences are statistically significant.
Correct Answer:
μ_new = μ_old
For classroom activity, students flip a coin 100 times. Expected heads ≈
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50
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100
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25
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0
Explanation
A fair coin has a 0.5 probability of landing heads. When flipping the coin 100 times, the expected number of heads is calculated as 100 × 0.5 = 50. This illustrates the concept of expected value in probability, helping students predict outcomes over repeated trials.
Correct Answer:
50
A teacher records the number of students late to class each day for 30 days. This follows a:
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Binomial distribution
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Normal distribution
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Poisson distribution
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Uniform distribution
Explanation
The number of students late per day is a count of events occurring within a fixed interval (a day). When events are rare or occur independently, the Poisson distribution models the probability of a given number of occurrences. Teaching this helps students understand appropriate probability models for count data versus proportions or continuous measurements.
Correct Answer:
Poisson distribution
For teaching critical value, at α = 0.05 two-tailed, z* ≈
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±1.645
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±1.96
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±2.33
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±2.58
Explanation
In a two-tailed test with significance level α = 0.05, the area in each tail is 0.025. The critical z-value that leaves 2.5% in the upper tail (and –2.5% in the lower tail) is approximately ±1.96. This value is used to determine the rejection region for hypothesis testing and is essential for teaching the link between confidence levels, significance levels, and critical values.
Correct Answer:
±1.96
For teaching confidence level, increasing from 95% to 99% will make the interval:
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Narrower
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Wider
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Unchanged
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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 plots height vs shoe size. r² = 0.64 means:
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64% of variability in height explained by shoe size
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64% causation
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36% error
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Correlation is 0.8
Explanation
The coefficient of determination (r²) represents the proportion of variance in the dependent variable that is explained by the independent variable. An r² of 0.64 means that 64% of the variability in height can be explained by shoe size. This helps students understand how well one variable predicts another, without implying causation.
Correct Answer:
64% of variability in height explained by shoe size
A confidence interval for difference in means (boys – girls) is (-5.2, 1.8). Conclusion:
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Boys score higher
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Girls score higher
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No significant difference
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Need p-value
Explanation
A confidence interval that includes zero indicates that the difference between groups could be zero, meaning there is no statistically significant difference at the given confidence level. Since the interval (-5.2, 1.8) spans zero, we cannot conclude that boys or girls have higher scores. This teaches students how to interpret confidence intervals for differences between groups.
Correct Answer:
No significant difference
Without replacement from the same bag, P(first red and second blue) =
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15/56
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15/64
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5/14
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3/14
Explanation
Without replacement, the probabilities change after the first draw. The probability of drawing a red marble first is 5/8. After removing one red marble, there are 7 marbles left, with 3 blue marbles. The probability of drawing a blue marble second is 3/7. Multiplying these together gives (5/8) × (3/7) = 15/56. This demonstrates how probabilities adjust when events are dependent.
Correct Answer:
15/56
A teacher uses spinners to model P(red then blue) = 3/8 × 4/7 =
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12/56
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7/15
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12/15
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3/56
Explanation
When calculating the probability of sequential dependent events without replacement, multiply the probability of the first event by the conditional probability of the second event. Here, the probability of red first is 3/8, and given one red is removed, the probability of blue next is 4/7. Multiplying these gives 3/8 × 4/7 = 12/56. This demonstrates the use of multiplication for dependent events in teaching probability.
Correct Answer:
12/56
Which sampling method is most likely to produce bias when surveying teens about social media use?
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Simple random sampling
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Stratified sampling
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Online poll on Instagram
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Cluster sampling
Explanation
An online poll on Instagram is likely to produce bias because it only reaches teens who use Instagram and are willing to respond. This self-selection excludes teens who do not use the platform or choose not to participate, leading to unrepresentative results. Teaching students about this helps them understand how sampling methods affect the reliability of survey data.
Correct Answer:
Online poll on Instagram
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