Statistics and regression

Paper labels are an unofficial, independently authored grouping, applied only where a question's own format genuinely matches a real paper convention (such as IB Mathematics AA's non-calculator/calculator split). They do not reproduce any exam board's real paper numbering or mark allocation, and uncertain questions are labelled general practice instead.

• 1A survey of 120 students records favourite study time (morning/evening) against year group (Year 12/Year 13). The observed frequencies give a calculated χ² test statistic of 4.83, and the critical value at the 5% significance level is 3.84. (a) State the null hypothesis for this test. (b) State whether favourite study time and year group are independent. (c) Justify your conclusion using both values. (d) State one condition required for a chi-squared test to be valid.Paper 1 styleMedium4 marksCalculator+
• 2Marking analysis: A learner attempts the following task: “A survey of 120 students records favourite study time (morning/evening) against year group (Year 12/Year 13). The observed frequencies give a calculated χ² test statistic of 4.83, and the critical value at the 5% significance level is 3.84. (a) State the null hypothesis for this test. (b) State whether favourite study time and year group are independent. (c) Justify your conclusion using both values. (d) State one condition required for a chi-squared test to be valid.” Their response addresses only this point: “States H0: favourite study time is independent of year group.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.Marking analysisMedium4 marksNo calculator+
• 3A café manager records daily temperature x (°C) and iced-drink sales y for six days: (18,20), (21,29), (24,38), (27,44), (30,55), (33,58). Using your GDC: (a) find the equation of the linear regression line of y on x. (b) State the value of Pearson's correlation coefficient r and interpret its strength. (c) Use your equation to estimate sales on a day with temperature 26°C. (d) Explain why using this equation to estimate sales at 5°C would not be appropriate.Paper 2 styleMedium5 marksCalculator+
• 4Marking analysis: A learner attempts the following task: “A café manager records daily temperature x (°C) and iced-drink sales y for six days: (18,20), (21,29), (24,38), (27,44), (30,55), (33,58). Using your GDC: (a) find the equation of the linear regression line of y on x. (b) State the value of Pearson's correlation coefficient r and interpret its strength. (c) Use your equation to estimate sales on a day with temperature 26°C. (d) Explain why using this equation to estimate sales at 5°C would not be appropriate.” Their response addresses only this point: “Uses the GDC regression feature to obtain y ≈ 2.51x − 25.6 (accept equivalent rounding).” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.Marking analysisMedium5 marksNo calculator+
• 5A factory's machine produces defective components independently with probability 0.04. In a random sample of 50 components, let X be the number of defective components, assumed to follow a binomial distribution. Using your GDC: (a) state the values of n and p. (b) Calculate P(X = 2). (c) Calculate P(X ≤ 1). (d) Calculate the expected number of defective components in the sample.Paper 2 styleMedium4 marksCalculator+
• 6Marking analysis: A learner attempts the following task: “A factory's machine produces defective components independently with probability 0.04. In a random sample of 50 components, let X be the number of defective components, assumed to follow a binomial distribution. Using your GDC: (a) state the values of n and p. (b) Calculate P(X = 2). (c) Calculate P(X ≤ 1). (d) Calculate the expected number of defective components in the sample.” Their response addresses only this point: “States n = 50 and p = 0.04.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.Marking analysisMedium4 marksNo calculator+