Unit 14: Statistical Tools and Techniques - Practice Quiz

1 In Bayesian statistics, what does a prior distribution represent?

2 What is the posterior distribution in Bayesian analysis?

3 Which quantity describes how probable the observed data are for different parameter values?

4 Bayes' theorem is commonly written as . What does represent?

5 What is the main purpose of Bayesian inference?

6 Which two components are combined to obtain a posterior distribution?

7 What does a Bayesian credible interval describe?

8 If new evidence strongly supports a parameter value, what generally happens to its posterior probability?

9 In Bayesian decision theory, what does a loss function measure?

10 A Bayes estimate is commonly selected to minimize which quantity?

11 Under squared-error loss, which posterior summary is the Bayes estimate?

12 Which Microsoft Excel function calculates the arithmetic mean of selected cells?

13 Which symbol normally begins a formula in Microsoft Excel?

14 Which Excel feature is commonly used to create a visual representation of data?

15 What is RStudio primarily used for?

16 Which R function calculates the mean of a numeric vector x?

17 In RStudio, where can commands be entered and executed interactively?

18 What does SPSS primarily help users perform?

19 In SPSS, which view displays observations in rows and variables in columns?

20 In SPSS, which view is used to define variable names, types, and labels?

21 A disease has prevalence . A diagnostic test has sensitivity and a false-positive rate of . What is the probability that a person has the disease given a positive result?

22 The probability of success has a prior. Before observing any data, what is the prior predictive probability of success on the next trial?

23 The prior odds in favor of model over are . If the likelihood ratio in favor of is , what are the posterior odds?

24 A 95% Bayesian credible interval for is . Which interpretation is appropriate?

25 A binomial success probability has prior . After observing 8 successes and 2 failures, what is the posterior distribution?

26 Using the posterior , what is the posterior predictive probability that the next trial is a success?

27 Suppose . A sample of size has mean , and the known observation variance is . What is the posterior mean of ?

28 A Bayes factor is obtained when comparing model with model . What does this value indicate?

29 If the posterior distribution is , what is the Bayes estimate of under squared-error loss?

30 A posterior distribution assigns probabilities , , and to , , and , respectively. What is the Bayes estimate under absolute-error loss?

31 A posterior distribution assigns probabilities , , and to parameter values , , and . What is the Bayes estimate under zero-one loss?

32 For a binary decision, a false positive costs and a false negative costs . If , when should action be selected?

33 Which Excel formula calculates the probability of exactly 7 successes in 10 independent trials when the success probability is ?

34 Values of a response variable are in cells B2:B21, and matching predictor values are in A2:A21. Which formula returns the least-squares slope?

35 A right-tailed test produces a test statistic of with degrees of freedom. Which Excel formula returns its p-value?

36 A data frame named survey contains variables score and hours. Which R command fits the model ?

37 A simulation in R gives different results each time it is run. Which command should be placed before the simulation to make the random results reproducible?

38 An R vector named draws contains simulated values from a posterior distribution. Which command computes an equal-tailed 95% credible interval?

39 A researcher wants to compare the mean exam scores of two unrelated teaching groups in SPSS. Which procedure is most appropriate?

40 In an SPSS multiple regression output, a predictor has coefficient and Sig. = 0.03. At significance level , which conclusion is appropriate?

41 For Bernoulli observations with successes in trials, consider the improper Haldane prior . Under which condition is the posterior distribution proper?

42 A disease has prevalence . A diagnostic test has sensitivity and specificity . Assuming these values apply to the tested population, what is the posterior probability of disease after a positive result?

43 Two sampling designs produce likelihoods satisfying , where does not depend on . If the same proper prior is used, which conclusion follows from the likelihood principle?

44 A Bernoulli probability has prior . After observing successes and failures, what is the posterior predictive probability that both of the next two trials are successes?

45 Observations are independent variables. The prior is , and a sample of size has mean . What is the posterior distribution of ?

46 For independent , use a Gamma prior with shape and rate . Four observations have total . What is the posterior predictive mean of one new observation?

47 Models and have prior probabilities and , respectively. The observed data yield Bayes factor . What is ?

48 For a continuous posterior distribution of , suppose the loss is when and when . Which posterior summary is the Bayes estimate?

49 The LINEX loss is . If and , what is the Bayes estimate?

50 The posterior probabilities of states and are and . Losses for actions , , and are respectively , , and across those states. Which action is Bayes-optimal?

51 A real-valued target has posterior distribution , but the reported action is constrained to . Under squared-error loss, what is the constrained Bayes action?

52 A binomial analysis produces posterior . Which Excel formulas return the equal-tailed credible interval?

53 Cells A2:A100 contain very negative log-weights . Which modern Excel formula stably computes while reducing numerical underflow?

54 In an Excel regression calculation, cell B2 contains a coefficient estimate and C2 its standard error. There are observations and predictors excluding the intercept. Which formula computes the usual two-sided -test p-value?

55 In R, lm(y ~ x*g) is fitted with factor level A as the reference for g. The estimated coefficients for x and x:gB are and . What is the fitted slope of when g == "B"?

56 For a fitted linear model fit, which R command obtains an interval for a single future response at predictor values stored in newdata, including irreducible observation noise?

57 An lm model in R was trained with factor levels A and B. A prediction data frame contains the previously unseen level C. Without manually changing levels or refitting, what normally happens when predict.lm is called?

58 SPSS Multiple Imputation produces estimates. The average within-imputation variance is , and the between-imputation variance is . Using Rubin's rules, what is the total variance?

59 An SPSS binary logistic model is , where is coded or . What is the odds ratio for a one-unit increase in among cases with ?

60 In an SPSS repeated-measures GLM, Mauchly's test is significant for a within-subject factor with more than two levels. Which result should be used for a conservative test of that within-subject effect?