Week 8 Summary (DSME5110F)
The rule: If p < α, reject H0; otherwise, do not reject Population Mean with Known σ
Population Mean (Unknown σ, t.test())
• One sample: t.test(x, alternative = c("two.sided", "less", "greater"), mu = mu0, conf.level = 0.95)
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• Two samples:
– Independent Samples:
∗ Non-stacked data: t.test(x, y, alternative = c(“two.sided”, “less”, “greater”), mu = mu0, var.equal = FALSE/TRUE,conf.level = 0.95)
∗ Stacked data: t.test(x ~ y, data = dataset_name, alternative = c(“two.sided”, “less”, “greater”), mu = mu0, var.equal = FALSE/TRUE,conf.level = 0.95)
∗ (check whether variances are equal or not: based on your intuition or use var.test())
– Paired Samples: t.test(x, y, alternative = c(“two.sided”, “less”, “greater”), mu =
mu0, paired = TRUE, conf.level = 0.95)
Population Proportion (prop.test())
• prop.test(x, n): x is number of successes, n is the sample size
– One sample: prop.test(x, n, p = p0, alternative = c(“two.sided”, “less”, “greater”),
conf.level = 0.95, correct = FALSE):
– Two samples: prop.test(c(x1, x2), c(n1, n2), alternative = c(“two.sided”, “less”,
“greater”), conf.level = 0.95, correct = FALSE)
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