Confidence Interval
When to use: Estimate a population mean or proportion.
Formula (mean): sample mean +/- critical value * (s/sqrt(n))
Steps:
1. Find sample mean, s, and n.
2. Find critical value (z* or t*).
3. Compute SE = s/sqrt(n).
4. Margin = critical value * SE.
5. CI = (sample mean - margin, sample mean + margin).
Tip: Use z* if n >= 30, t* if n < 30 and sigma unknown.
Hypothesis Testing
When to use: Testing a claim about a population mean or proportion.
Steps:
1. State H0 (null) and Ha (alternative).
2. Choose alpha (like 0.05).
3. Calculate test statistic: t = (sample mean - claimed mean)/(s/sqrt(n)).
4. Find p-value.
5. Decision: If p-value < alpha, reject H0.
Tip: Sketch left-tailed, right-tailed, or two-tailed tests!
Central Limit Theorem (CLT)
When to use: Sampling distribution of sample mean.
Key Points:
- For large n (>=30), sample means are approximately normal.
- Mean = population mean, SE = sigma/sqrt(n).
Steps:
1. Compute SE.
