good stats
CHAPTER 1: Descriptive Stats
Question: If a histogram is skewed right, where is the mean relative to the median?
Answer: Mean is greater than median (mean > median)
Question: If a histogram is skewed left, where is the mean relative to the median?
Answer: Mean is less than median (mean < median)
Question: Which is more resistant to outliers: mean or median?
Answer: Median
Question: What does a boxplot show you that a histogram doesn't?
Answer: Exact five-number summary (Min, Q1, Median, Q3, Max) and outliers
Question: Using the IQR method, a value is an outlier if it falls below what?
Answer: Q1 - 1.5 × IQR
Question: Using the IQR method, a value is an outlier if it falls above what?
Answer: Q3 + 1.5 × IQR
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CHAPTER 2: Probability Concepts
Question: If two events are mutually exclusive, can they be independent?
Answer: No, not unless one has probability zero. Mutually exclusive means P(A∩B)=0, so P(A|B)=0 which does not equal P(A)
Question: What is the difference between mutually exclusive and independent events?
Answer: Mutually exclusive means events cannot happen together. Independent means one event does not affect the probability of the other
Question: Does P(A|B) equal P(B|A) in general?
Answer: No, only when P(A) equals P(B)
Question: If P(A)=0.5, P(B)=0.5, and P(A∩B)=0.25, are A and B independent?
Answer: Yes, because P(A)×P(B)=0.25 which equals P(A∩B)
Question: In a tree diagram, how do you find the probability of reaching a final branch?
Answer: Multiply the probabilities along all branches leading to that outcome
Question: What is the probability of neither A nor B occurring?
Answer: 1 minus P(A union B), which is 1 minus [P(A)+P(B)-P(A∩B)]
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CHAPTER 3: Discrete Distribution Recognition
Question: You count the number of defective items in a sample of 10 drawn without replacement from a batch of 100. What distribution?
Answer: Hypergeometric (sampling without replacement from a finite population)
Question: You count the number of customers arriving at a store in one hour. What distribution?
Answer: Poisson (counts of events over time or space)
Question: You flip a coin 20 times and count the number of heads. What distribution?
Answer: Binomial (fixed number of trials, independent, constant probability)
Question: You flip a coin until you get your first head. What distribution?
Answer: Geometric (number of trials until first success)
Question: What is the key clue that tells you to use Poisson instead of Binomial?
Answer: No fixed number of trials; counting events over time/area rather than number of attempts
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CHAPTER 4: Normal & Continuous Distributions
Question: For any continuous distribution, what is P(X equals an exact value)?
Answer: Zero. Only intervals have probability for continuous distributions
Question: What are the mean and standard deviation of the standard normal distribution?
Answer: Mean = 0, Standard deviation = 1
Question: About what percentage of data falls within 2 standard deviations of the mean in a Normal distribution?
Answer: Approximately 95%
Question: About what percentage of data falls within 1 standard deviation of the mean in a Normal distribution?
Answer: Approximately 68%
Question: What type of real-world phenomenon is often modeled by the exponential distribution?
Answer: Waiting times or lifetimes (time until next event occurs)
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CHAPTER 5: Sampling & Central Limit Theorem
Question: As sample size increases, what happens to the sampling distribution of the sample mean?
Answer: It becomes more Normal (CLT) and narrower (smaller standard error)
Question: Does the Central Limit Theorem apply to the sample median?
Answer: No, the CLT applies specifically to the sample mean
Question: If the population is Normal, what is the shape of the sample mean's distribution for any sample size?
Answer: Normal (even for n=1)
Question: What is the standard deviation of the sample mean called?
Answer: Standard error
Question: If sample size increases, does the standard error increase or decrease?
Answer: Decrease (standard error = sigma divided by square root of n)
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CHAPTER 6: Point Estimation Concepts
Question: What does unbiased mean in plain English?
Answer: On average, the estimator hits the true parameter value (no systematic overestimation or underestimation)
Question: Is the sample variance s-squared unbiased for the population variance sigma-squared?
Answer: Yes
Question: Is the sample standard deviation s unbiased for the population standard deviation sigma?
Answer: No (this is a common trick question)
Question: What does a consistent estimator mean?
Answer: As sample size increases, the estimator gets closer and closer to the true parameter value
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CHAPTER 7: Confidence Interval Interpretation
Question: True or false: A 95% confidence interval means there is a 95% probability the parameter is in this specific interval.
Answer: False. The parameter is fixed. 95% refers to the long-run capture rate of the method.
Question: If you increase the confidence level from 90% to 99%, what happens to the interval width?
Answer: It gets wider
Question: If you increase the sample size, what happens to the confidence interval width?
Answer: It gets narrower
Question: A 95% confidence interval for the population mean is (10, 20). Does this mean 95% of the data falls between 10 and 20?
Answer: No. The confidence interval is about the mean, not individual data points.
Question: What is the difference between margin of error and interval width?
Answer: Interval width = 2 × Margin of Error
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CHAPTER 8: Hypothesis Testing
Question: In plain English, what is a p-value?
Answer: The probability of observing data as extreme as (or more extreme than) what you got, assuming the null hypothesis is true
Question: A small p-value provides evidence for or against the null hypothesis?
Answer: Against the null hypothesis (reject H0)
Question: If you fail to reject the null hypothesis, does that mean the null hypothesis is true?
Answer: No. It means there is not enough evidence to conclude it is false.
Question: What is a Type I error?
Answer: False positive - rejecting the null hypothesis when it is actually true
Question: What is a Type II error?
Answer: False negative - failing to reject the null hypothesis when it is actually false
Question: Which type of error is controlled by the significance level alpha?
Answer: Type I error
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CHAPTER 9: Two-Sample Inference
Question: Same subjects measured before and after a treatment — which test should you use?
Answer: Paired t-test
Question: Two separate groups (treatment vs control) with different subjects — which test should you use?
Answer: Two-sample t-test (independent samples)
Question: For a two-proportion z-test, what is the minimum sample size requirement?
Answer: At least 5 successes and 5 failures in each group
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CHAPTER 12: Regression
Question: A slope of zero means what about the relationship between X and Y?
Answer: There is no linear relationship between X and Y
Question: If R-squared equals 0.64, what percentage of variation in Y is explained by X?
Answer: 64%
Question: If R-squared equals 0.64 and the slope is positive, what is the correlation r?
Answer: 0.8 (the square root of 0.64, with the same sign as the slope)
Question: Which is wider: a confidence interval for the mean response or a prediction interval for a new observation?
Answer: Prediction interval (it is always wider)
Question: What does the residual standard error estimate?
Answer: Sigma, the typical distance of points from the regression line
Question: If the slope is positive, what sign does the correlation r have?
Answer: Positive (same sign as the slope)
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TRAP QUESTIONS (Most Commonly Missed)
Question: True or false: "We accept the null hypothesis" is correct statistical wording.
Answer: False. Always say "fail to reject the null hypothesis" — never "accept"
Question: True or false: A 95% confidence interval means 95% of sample means fall in this interval.
Answer: False. It means 95% of confidence intervals from repeated samples will contain the population mean.
Question: True or false: The sample standard deviation s is an unbiased estimator of the population standard deviation sigma.
Answer: False (this is a very common trick question)