SME
Grade 12 Math
Statistics
Sampling distributions and the central limit theorem
Main lesson
Sampling distribution of a proportion
Use this for “40% of voters agree. In a sample of 150, what is P(p̂ > 0.46)?”
Mean and spread of a binomial count
Use this for “In 40 trials with p = 0.25, find the mean and standard deviation of the count” (up to 40 trials).
The central limit theorem, simulated
Use this for “Wait times are skewed right with mean 4 minutes. How are the means of samples of 30 spread?”
Sample means and sums with any σ
Use this for “Bags of rice weigh 2 kg on average with σ = 0.12 kg. Find the chance that 36 bags average over 2.03 kg, or weigh over 73.08 kg in all.”
Confidence intervals for a mean and a proportion
Main lesson
Confidence interval for a mean, σ unknown
Use this for “10 plants average 52 cm with s = 8 cm. Find a 95% confidence interval for μ.”
Confidence interval for a proportion
Use this for “240 of 400 people said yes. Find a 95% confidence interval for p.”
Sample size for a margin of error
Use this for “How many people must be asked for a 95% margin of 3 points?”
What “95% confident” means
Use this for “Draw 50 samples: how many of the 95% intervals should capture μ?”
Hypothesis tests for one and two samples
Main lesson
One-mean z-test
Use this for “Is the mean less than μ₀?” (or more than, or different from) with σ known.
One-mean t-test
Use this for “A sample of 16 has mean 496 g and s = 8 g. Is the mean different from 500 g?”
Matched pairs t-test
Use this for “Twelve students gained 2.5 points on average after a review, s = 3.2. Did the review change scores?”
Two-proportion z-test
Use this for “84 of 150 people sent a reminder voted, against 66 of 150 who were not. Is there a difference?”
Two-sample t-test for means
Use this for “Do two groups have different means?” from two independent samples.
Which alternative hypothesis?
Use this for “Write H₀ and Hₐ for the claim that the new bulbs last longer.”
Type I or Type II error?
Use this for “Name a Type I and a Type II error for this test.”
Chi-square tests for goodness of fit and independence
Inference for the slope of a regression line
Main lesson
Confidence interval for the slope
Use this for “b = 0.8 and SEb = 0.25 from 20 points. Find a 95% confidence interval for the slope.”
Is the correlation significant?
Use this for “r = 0.6 for 18 pairs of data. Is the correlation significant at 0.05?”
The standard error of the slope
Use this for “The residuals have s = 2, the x values have sₓ = 1.5 and n = 10. Is b = 1.2 significant?”
Analysis of variance (ANOVA) and the F distribution
Main lesson
Three groups from their means and SDs
Use this for “Three groups of 5 have means 10, 14 and 12 and SDs 2, 3 and 2. Do the means differ?”
Comparing two variances
Use this for “Two samples of 16 have SDs 6 and 4. Are the population variances different?”
Which test fits the question?
Use this for “Do the mean scores of three classes differ? Which test do you use?”