Interval Estimation & Hypothesis testing
14 important questions on Interval Estimation & Hypothesis testing
What is estimation in statistics?
- Point estimate: a single best guess (e.g. sample mean Xˉ)
- Interval estimate: a range that likely contains the true value (confidence interval)
What is the standard error (SE)?
Smaller SE → more precise estimates.
What is a confidence interval (CI) for a population mean μ (σ known)?
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What is a CI for μ (σ unknown)?
→ df=n−1df = n - 1
What does the confidence level (e.g. 95%) mean?
If we repeated sampling many times, 95% of the confidence intervals would contain the true population mean μ.
It does not mean there’s a 95% chance that μ lies in your interval — μ is fixed!
What is the formula for a CI for a population proportion p?
What is hypothesis testing?
What are the steps of hypothesis testing?
- State hypotheses
- Choose significance level (alpha)
- Calculate test statistic
- Find critical value or p-value
- Conclude (Reject or Fail to Reject H0)
What is the null hypothesis (H0)
Example: H0 : μ = 10
What is the alternative hypothesis (H1)?
Examples:
H1:μ≠10 -> two-tailed
H1:μ>10 -> right-tailed
H1:μ<10 -> left-tailed
What is the test statistic for a population mean (σ known)?
What is the test statistic for a population mean (σ unknown)?
What is the rejection region?
Example: for α = 0.05, two-tailed → reject if |Z| > 1.96.
What is the relationship between CI and hypothesis testing?
If it lies inside, fail to reject H0H_0
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