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Statistics: lesson checks flashcards

This deck has 10 check-yourself questions and 8 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Years 12–13 · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• A larger sample automatically makes the results representative.Spot the error
• A factory's 1200 workers are 900 full-time and 300 part-time. Describe how to take a sample of 60, stratified by contract type.Check
• Adding 5 to every value in a data set increases the standard deviation.Spot the error
• Ten values have Σx = 120 and Σx² = 1560. Find the mean and the standard deviation.Check
• A data set has Q₁ = 15 and Q₃ = 27. Using the 1.5 × IQR rule, decide whether the value 48 is an outlier.Check
• A regression line for crop yield y (tonnes) against rainfall x (cm), from data with 20 ≤ x ≤ 60, is y = 1.2 + 0.08x. A farmer asks for the predicted yield when x = 100. What do you say?Check
• Mutually exclusive events are independent, since they have nothing to do with each other.Spot the error
• P(A) = 0.6, P(B) = 0.3, and A and B are mutually exclusive. Write down P(A ∩ B) and find P(A ∪ B).Check
• P(A|B) and P(B|A) are the same thing written two ways.Spot the error
• P(A ∩ B) = 0.12 and P(B) = 0.4. Find P(A|B), and state what P(A) would have to equal for A and B to be independent.Check
• Ten percent of a batch are faulty, so in a sample of 10 exactly one will be faulty.Spot the error
• X ~ B(20, 0.15). Write P(X ≥ 5) in a form a calculator's cumulative function accepts, and state the value of P(X = 0) as a power.Check
• About half of a normal population lies more than one standard deviation from the mean.Spot the error
• X ~ N(μ, 6²) and P(X < 82) = 0.975. Use z = 1.96 to find μ.Check
• Rejecting the null hypothesis proves the alternative is true.Spot the error
• X ~ B(30, 0.2) under H₀, and the critical region for a one-tailed test is X ≥ 11 with P(X ≥ 11) = 0.0256. State the actual significance level and what it measures.Check
• The sample mean of n readings has the same standard deviation as a single reading.Spot the error
• Readings are N(μ, 9) and H₀ sets μ = 50. A sample of 36 has mean 49.2. Find the z-value for testing H₁: μ < 50.Check

The lessons these cards come from

• Conditional probability
• Correlation and regression
• Hypothesis testing with the binomial
• Hypothesis testing: correlation and the normal
• Measures of location and spread
• Probability and Venn diagrams
• Representing and interpreting data
• Sampling and the large data set
• The binomial distribution
• The normal distribution

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