Probability Distributions & Descriptive Statistics
22 important questions on Probability Distributions & Descriptive Statistics
What are descriptive vs inferential statistics?
Inferential: draw conclusions about a population from a sample (estimating national average income)
What is a population and what is a sample?
What are the most common probability distributions?
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What is the mean, variance, and standard deviation?
What is the Central Limit Theorem (CLT)?
Xˉ\bar{X} is approximately normally distributed:
✅ This allows us to use normal theory for inference even when the population isn’t normal.
What is a point estimate and an interval estimate?
Formula for a confidence interval (for μ):
What is hypothesis testing?
What is the 5-step plan?
2️⃣ Choose α (significance level)
3️⃣ Calculate test statistic (z or t)
4️⃣ Compare with critical value or find p-value
5️⃣ Conclude (reject or not reject H0H_0 )
What is α (alpha level)?
What is simple linear regression?
Y i = β 0 + β 1 X i + ϵ i
β0 : intercept
β1 slope (effect of X on Y)
ϵi random error term
How do you interpret β1?
Example: if β₁ = 2.5 → each extra euro spent on ads increases sales by 2.5 units.
What is R² (coefficient of determination)?
What is the F-test in regression?
H0:β1=β2=...=0H_0: \beta_1 = \beta_2 = ... = 0 If p < α, the model explains significant variation in Y.
What happens if assumptions are violated?
- Non-linear → model misspecification
- Unequal variance → biased standard errors
- Multicollinearity → unstable β estimates
→ check with plots and VIF (Variance Inflation Factor)
What are the main regression assumptions?
2. Independence of errors
3. Homoscedasticity (equal variance)
4. Normality of residuals
5. No multicollinearity (in MLR)
What is ANOVA in regression?
SST = SSR + SSE
- SST: total variation
- SSR: explained by regression
- SSE: unexplained (residual)
What is the difference between t-test and F-test?
- t-test → one coefficient (is β₁ ≠ 0?)
- F-test → multiple coefficients at once (is the model significant?)
What are confidence intervals used for in regression?
What reduces sampling error?
What is a Type I and Type II error?
II = failing to reject a false H0
What is the standard error of the mean?
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