C883 Statistics and Probability for Secondary Mathematics Teaching

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Free C883 Statistics and Probability for Secondary Mathematics Teaching Questions

1.

A teacher uses a frequency table for survey data on favorite subjects. The relative frequency for math is 0.35. What does this mean for lesson planning?

  • 35% prefer math – emphasize real-world applications​

  • 65% dislike math – avoid group work​

  • Data is biased​

  • Use pie chart only

Explanation

Explanation
Relative frequency represents the proportion of the total data that falls into a specific category. A relative frequency of 0.35 for math means that 35% of students indicated math as their favorite subject. This information helps the teacher plan lessons that engage a significant portion of the class, such as emphasizing real-world applications to make math more appealing and relevant to those students.
Correct Answer:
35% prefer math – emphasize real-world applications
2.

To teach blinding, a study on new math app vs textbook should:

  • Let students choose group​

  • Hide which group uses app from scorers​

  • Tell teachers everything​

  • Use small sample

Explanation

Explanation
Blinding involves keeping certain participants or evaluators unaware of group assignments to prevent bias in measurement or scoring. In this example, hiding which group uses the app from those scoring tests ensures that expectations do not influence results. Teaching blinding emphasizes objective assessment in experimental studies.
Correct Answer:
Hide which group uses app from scorers
3.

The five-number summary for a data set is 10, 20, 30, 40, 50. The boxplot will show:

  • No whiskers​

  • Symmetric box​

  • Skewed left​

  • Outliers

Explanation

Explanation
The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. In this case, the values are evenly spaced: 10, 20, 30, 40, 50. A boxplot based on these numbers will be symmetric because the distances between the quartiles and the median are equal, and the whiskers on either side are of equal length. This indicates a perfectly balanced, symmetric distribution with no skew or outliers.
Correct Answer:
Symmetric box
4.

In a back-to-back stem plot for two classes, it compares:

  • Distributions side-by-side​

  • Means only​

  • Individual scores hidden​

  • Correlation

Explanation

Explanation
A back-to-back stem-and-leaf plot displays two data sets on opposite sides of a common stem, allowing for direct visual comparison of their distributions. It preserves individual data values while showing overall patterns, making it an effective tool for comparing two classes’ performance or other paired data sets in a clear and interpretable way.
Correct Answer:
Distributions side-by-side
5.

A test statistic z = 2.1, p-value = 0.0357. At α = 0.01:

  • Reject H₀​

  • Fail to reject H₀​

  • Accept H₀​

  • Recalculate

Explanation

Explanation
The decision rule for hypothesis testing is to reject the null hypothesis if the p-value is less than the significance level α. Here, p-value = 0.0357, which is greater than α = 0.01. Therefore, there is not enough evidence to reject H₀, and the correct decision is to fail to reject it. This teaches students how to interpret p-values relative to significance levels.
Correct Answer:
Fail to reject H₀
6.

In a class survey, 60% play sports and 40% play music. If 25% do both, P(only sports) =

  • 35%​

  • 60%​

  • 75%​

  • 25%

Explanation

Explanation
The probability of students playing only sports is calculated by subtracting those who do both activities from the total who play sports. Since 60% play sports and 25% play both sports and music, the percentage who play only sports is 60% – 25% = 35%. This teaches students how to apply the principle of inclusion and exclusion in probability.
Correct Answer:
35%
7.

For teaching binomial to normal approximation, need:

  • np ≥ 10 and n(1-p) ≥ 10​

  • n ≥ 30 only​

  • p = 0.5​

  • Continuity correction never

Explanation

Explanation
The normal approximation to the binomial is appropriate when both np and n(1–p) are at least 10. This ensures the binomial distribution is sufficiently symmetric and continuous-like. Teaching this criterion helps students understand when it is reasonable to use normal approximation for probability calculations.
Correct Answer:
np ≥ 10 and n(1-p) ≥ 10
8.

A teacher runs a 2-sample t-test: t = –2.45, df = 38, p = 0.019. At α = 0.01:

  • Reject H₀​

  • Fail to reject H₀​

  • Accept H₀​

  • Increase sample

Explanation

Explanation
The p-value (0.019) is greater than the significance level α = 0.01, so there is insufficient evidence to reject the null hypothesis. Teaching this reinforces the interpretation of p-values relative to chosen significance levels and proper decision-making in hypothesis testing.
Correct Answer:
Fail to reject H₀
9.

For teaching effect size, a Cohen’s d = 0.8 means:

  • Large difference​

  • Moderate​

  • Small​

  • No difference

Explanation

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
10.

For teaching percentile rank, a score at the 75th percentile means:

  • 75% scored higher​

  • 75% scored lower or equal​

  • The score is 75% of maximum​

  • Outlier

Explanation

Explanation
A percentile rank indicates the percentage of scores in a data set that fall below or equal to a particular value. A score at the 75th percentile means that the student scored better than or equal to 75% of all the other scores, and only 25% scored higher. It helps teachers explain relative performance within a group rather than the raw score itself.
Correct Answer:
75% scored lower or equal

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