• For each possible gestation time, what proportion of babies in the population had that gestation time?

• Population mean: 38.8 weeks
• Population standard deviation: 2.6 weeks
• About 95% of babies in the population had gestation times between \((38.8 - 2 * 2.6)\) weeks and \((38.8 + 2 * 2.6)\) weeks

• For each possible length of gestation time, what proportion of babies in the sample had that gestation time?

babies_sample <- sample_n(babies, size = 30)

• Sample mean: 38.7 weeks
• Sample standard deviation: 2.2 weeks
• About 95% of babies in the sample had gestation times between \((38.7 - 2 * 2.2)\) weeks and \((38.7 + 2 * 2.2)\) weeks

• The sampling distribution is the distribution of values of the sample mean, across all different samples of a certain size \(n\).
• If \(n\) is large enough, \(\bar{X} \sim \text{Normal}(\mu, \sigma/\sqrt{n})\)

• Population mean: 38.8 weeks
• Population standard deviation: 2.6 weeks
• About 95% of samples of size 30 have sample mean gestation times between \((38.8 - 2 * \frac{2.6}{\sqrt{30}})\) and \((38.8 + 2 * \frac{2.6}{\sqrt{30}})\)

• (best guess of population mean) \(\pm\) (margin of error)
• \(\bar{x} \pm 2 s / \sqrt{n}\)

• Sample mean: 38.7 weeks
• Sample standard deviation: 2.2 weeks
• We are "95% Confident" that the population mean gestation time is between \((38.7 - 2 * \frac{2.2}{\sqrt{30}})\) and \((38.7 + 2 * \frac{2.2}{\sqrt{30}})\)
• "95% Confident" means: 95% of intervals constructed this way from different samples will contain the population mean