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ScotlandStatistics

Statistical Inference

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you estimate a population mean from a sample and express how confident you are?

Calculate point estimates of a population mean and variance, construct and interpret confidence intervals for a population mean using the normal and Student's t-distributions, and construct a confidence interval for a population proportion.
A focused answer to the SQA Advanced Higher Statistics estimation content: point estimates of the population mean and variance, confidence intervals for a mean using the normal distribution and Student's t-distribution, the role of degrees of freedom, and confidence intervals for a population proportion.
13 min answer →

How does the sample mean vary from sample to sample, and why is it approximately normal?

Describe the sampling distribution of the sample mean, calculate its mean and standard error, and state and apply the central limit theorem to find probabilities for a sample mean.
A focused answer to the SQA Advanced Higher Statistics sampling distributions content: the sampling distribution of the sample mean, its expected value and standard error, the central limit theorem, and how to find probabilities for a sample mean by standardising.
12 min answer →

How do you choose a representative sample from a population, and why does the method matter?

Describe and apply the main sampling methods, including simple random, systematic and stratified sampling, distinguish a sample from a population and a statistic from a parameter, and explain how a poor sampling method introduces bias.
A focused answer to the SQA Advanced Higher Statistics sampling content: the difference between a population and a sample and a parameter and a statistic, simple random, systematic and stratified sampling, how to carry each out, and how a poor sampling frame or method introduces bias.
11 min answer →

How do you plan, carry out and communicate a complete statistical investigation?

Conduct a statistical investigation that draws together the skills of the course: pose a question, plan and collect data, select and apply appropriate analysis, and communicate justified conclusions with their limitations.
An overview of the statistical investigation in SQA Advanced Higher Statistics: how the skills of design, analysis and inference are combined to pose a question, collect and analyse data, and communicate justified conclusions with their limitations, as examined in the question papers.
10 min answer →