Probability Distributions and Hypothesis Testing - One Line Questions

1. What are the degrees of freedom for a Chi-Squared test of independence with 'r' rows and 'c' columns? — (r-1)(c-1)
2. The sum of probabilities for all possible outcomes in any probability distribution must equal: — 1
3. The standard normal distribution has a mean of: — 0
4. The standard normal distribution has a standard deviation of: — 1
5. The F-distribution is used for comparing: — Two population variances
6. In hypothesis testing, what is the null hypothesis (H₀) typically stated as? — A statement of no effect or no difference
7. Which theorem states that the sampling distribution of the sample mean will approach a normal distribution as the sample size gets larger, regardless of the population distribution? — Central Limit Theorem
8. What is the probability of committing a Type I error called? — Significance level (α)
9. Which type of probability distribution is characterized by a bell-shaped curve and is symmetric around its mean? — Normal Distribution
10. Which of the following distributions is characterized by two parameters: mean (μ) and standard deviation (σ)? — Normal Distribution
11. A p-value of 0.01 is obtained in a hypothesis test with α = 0.05. What is the conclusion? — Reject H₀
12. If the p-value is less than the significance level (α), what action is typically taken regarding the null hypothesis? — Reject the null hypothesis
13. A two-tailed hypothesis test is used when the alternative hypothesis states that a parameter is: — Not equal to a value
14. What test is used to determine if there is a statistically significant difference between the means of two related groups (e.g., before and after treatment on the same subjects)? — Paired t-test
15. When comparing the means of three or more independent groups, which statistical test is most appropriate? — One-way ANOVA
16. In hypothesis testing, if the sample size increases, what generally happens to the width of the confidence interval (assuming other factors remain constant)? — It decreases
17. The power of a statistical test is defined as the probability of: — Correctly rejecting a false null hypothesis
18. In ANOVA (Analysis of Variance), the F-statistic is the ratio of: — Mean Square Treatment to Mean Square Error
19. The Chi-Squared (χ²) distribution is primarily used for testing hypotheses about: — Goodness-of-fit and independence of categorical variables
20. Which distribution is characterized by skewness and is often used for modeling waiting times? — Exponential Distribution
21. Which distribution is used for modeling the time until an event occurs in a Poisson process? — Exponential Distribution
22. Which probability distribution is often used to approximate the binomial distribution when 'n' is large and 'p' is small? — Poisson Distribution
23. What test is used to determine if there is a statistically significant difference between the means of two independent groups? — Independent samples t-test
24. The Chi-Squared goodness-of-fit test is used to determine if a sample distribution matches a: — Particular theoretical distribution
25. The t-distribution is similar to the normal distribution but has heavier tails and is used when: — Population variance is unknown and sample size is small
26. The alternative hypothesis (H₁) is a statement that contradicts the: — Null hypothesis
27. The Poisson distribution is often used to model the number of events occurring within a fixed interval of what? — Time or space
28. In the context of normal distribution, what is the standard deviation of the sampling distribution of the sample mean called? — Standard error
29. Which distribution is commonly used for hypothesis testing about the variance of a normally distributed population? — Chi-Squared distribution
30. The distribution of the sample variance from a normally distributed population follows which distribution? — Chi-Squared distribution
31. What type of test is appropriate for comparing a sample proportion to a hypothesized population proportion? — Z-test for proportions
32. The exponential distribution has a single parameter, usually denoted by λ, which represents: — The rate parameter
33. A Type I error in hypothesis testing occurs when: — The null hypothesis is incorrectly rejected when it is true
34. A Type II error occurs when: — The null hypothesis is incorrectly accepted when it is false
35. What is the parameter 'λ' (lambda) in a Poisson distribution? — The average rate of events
36. In a binomial distribution, what does 'n' typically represent? — The number of trials
37. What does a p-value represent in hypothesis testing? — The probability of observing the sample data (or more extreme) if the null hypothesis is true
38. In hypothesis testing, a critical region is: — The range of values for which we reject the null hypothesis
39. Which of the following is NOT a condition for using the Z-test for a single proportion? — The population is normally distributed
40. When conducting a one-sample t-test, what is the null hypothesis typically stating? — The population mean is equal to a hypothesized value
41. What does the term 'degrees of freedom' generally refer to in statistical distributions? — The number of independent pieces of information used to estimate a parameter
42. What is the primary assumption for using the standard t-test for independent samples? — The two populations have equal variances
43. A 95% confidence interval means that: — If we were to take many samples and construct intervals, 95% of them would contain the true population parameter
44. What is the primary purpose of hypothesis testing in statistics? — To make decisions about population claims based on sample data
45. What is the fundamental principle behind hypothesis testing? — To disprove the null hypothesis or find insufficient evidence to reject it
46. What is the primary purpose of a confidence interval? — To provide a range of plausible values for a population parameter
47. What is the relationship between the variance and the mean in a Poisson distribution? — Variance is equal to the mean
48. What is the primary difference between a Z-test and a t-test when comparing two population means? — Z-test is used when population standard deviations are known or sample sizes are large, t-test is used when they are unknown and sample sizes are small
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