A-Level Maths: Statistics (Year 2)

Measure linear relationships with Pearson's product moment correlation coefficient, or r, on a -1 to 1 scale, identifying positive, negative, or no correlation and linking nonlinear data to regression.

Calculate the product moment correlation coefficient using a calculator in two-variable data, interpret R in the -1 to 1 range, and identify strong positive or negative correlations.

Compute the regression line equation from data with a calculator to predict weight from height. Interpret the intercept and gradient, discuss correlation strength, and note extrapolation limits for reliable predictions.

Learn how to conduct hypothesis tests for correlation, distinguish real relationships from random flukes, and use correlation coefficients and critical values to assess significance with a sample size of 30.

Learn to perform a one-tailed hypothesis test for population correlation rho using sample r, compare to the critical value, and interpret results with an example on plant water and height.

Explore a one-tailed hypothesis test for correlation using chicken weights and eggs. Interpret the negative sample correlation and conclude there is not enough evidence to reject H0 at 2.5%.

Learn to perform a two-tailed hypothesis test for correlation, with H0: ρ=0 and H1: ρ≠0. Split the 5% significance into 2.5% tails and compare r to the critical value.

Study non-linear data using exponential and polynomial models, linearizing with log transforms and the model C = A B^T, and interpret B as percent change per time unit.

Examine non-linear, polynomial data by logging both axes, derive C = 6.17 W^0.5, and note a strong correlation r = 0.956 supporting an excellent model.

Explore set notation for probability, including intersections, unions, complements, and inclusive or, using Venn diagrams, then apply to medal-count problems, independence, and mutual exclusivity, paving the way for conditional probability.

Develop an intuitive understanding of conditional probability using Venn diagrams and tables to compute events like long hair given boy and red given Italian, before formalizing the formula.

Learn the conditional probability formula with a Venn diagram, and see its connection to Bayes' theorem for non-independent events, noting independence makes P(A|B)=P(A).

Apply conditional probability with tree diagrams to update beliefs, such as sunny weather given tennis. Explore two scenarios with draws and Bayes thinking.

Explore conditional probability in a medical testing scenario: a rare disease with 1% prevalence and a 95% accurate test show why a positive result yields only 16% probability of disease.

Learn to apply conditional probability to binomial distributions, using P(A|B)=P(A∩B)/P(B) and calculator methods, with examples of 20 trials (p=0.4) and 30 shots.

Explore the normal distribution and its bell curve for continuous data, mean, and standard deviation. See how areas under the curve yield probabilities and properties shared by all normal distributions.

Explore the 68-95-99.7 rule for normal distributions, and see how within one, two, and three standard deviations the data falls (about 68%, 95%, 99.7%).

Learn to calculate normal distribution probabilities using a Casio calculator, with mean and standard deviation, handling lower and upper bounds for practical questions like bulb lifetimes and expected counts.

Explore the inverse normal distribution, using mean and standard deviation to find cutpoints and percentiles. Learn to use the inverse normal function and left-area interpretation on calculators.

Discover how to find unknown standard deviations using the standardized normal distribution and inverse normal calculations, with examples involving oranges and popcorn and top 10 percent cutoffs.

Learn to compute an unknown mean from a known standard deviation using z-scores and inverse normal, with examples involving the top quartile and a negative mean.

Solve for unknown mean and standard deviation using percentile information and the standard normal distribution, via two equations and simultaneous solutions.

Explore using the normal distribution to approximate the binomial for large trials, when p is near 0.5, and learn the mean np and variance np(1-p).

Learn how to use the normal distribution to approximate binomial probabilities when n is large and p is near 0.5, including continuity corrections, and how to apply it.

Use the normal approximation to the binomial by setting the mean to np and variance to np(1-p), applying continuity correction, and evaluating hypothesis tests at a chosen significance.

Carry out a normal hypothesis test for a mean change, using the sampling distribution of the mean, and significance levels to judge if 71 from n=10 is surprising.

Lay out a one-tailed normal hypothesis test for a change, state null and alternative means, compute sampling distribution, and decide whether to reject H0 with 5% significance.

Use a two-tailed normal hypothesis test to check if the mean coffee weight changed from 301, with n 30, sample mean 300.7, and sd 0.6.

Identify the 5% left-tail critical region for a one-tailed normal test of dolphin weights (n=12, mean=140, sd=14). If the sample mean falls below 133.35, conclude the mean has dropped.

Learn to form distributions from normal data by converting to binomial probabilities, solving at least questions, and using calculator tools, with examples involving weight and height from the normal distribution.

Master conditional probability with the normal distribution, using a mean of 40 and a standard deviation of sqrt(75) to compute P(X<25|X<30) and P(X>35|X<50).

Explore Edexcel June 2023 paper 3 statistics with worked examples on Venn diagrams, binomial tests, hypothesis testing, normal distributions, data cleaning, and curve modeling.