Inference using Normal and t-distributions

Worked examples (6)

• 1Choosing the right test
• 2Computing the unbiased variance estimate
• 3A complete one-tailed test from raw totals
• 4A two-tailed test — watch the table column
• 5Building the test from a raw data list
• 6Working backwards — the critical sample mean

Model answers (6)

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Worked examples (6)

• 1Pooled variance from two sample variances
• 2Equal sample sizes — pooling reduces to a simple average
• 3Pooled variance from raw data (sums)
• 4Pooled variance when one sample gives a standard deviation
• 5Pooled variance from two raw data sets
• 6Pool, then build the two-sample standard error

Model answers (6)

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Worked examples (6)

• 1Forming H₀ and H₁ for a difference of means
• 2Deciding: paired or two-sample?
• 3Full two-sample pooled t-test
• 4Full paired t-test
• 5Known-variance normal (z) test
• 6Testing a specified difference (μ₁ − μ₂ ≠ 0)

Model answers (6)

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Worked examples (6)

• 1A 95% z-interval with known variance
• 2Interpreting a confidence interval in words
• 3A t-interval from raw data
• 4Large sample with unknown variance
• 5A pooled t-interval for a difference of means
• 6Sample size needed to halve the width

Model answers (6)

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