Unit 5: Role of Statistics in Data Science - Practice Quiz

1 What is the main purpose of hypothesis testing?

2 What does the null hypothesis usually state?

3 What does the alternative hypothesis generally propose?

4 A result is commonly considered statistically significant when which condition is met?

5 What is a Type 1 error?

6 What is a Type 2 error?

7 What does a p-value measure?

8 If and , what is the usual decision?

9 What is ANOVA mainly used to compare?

10 What does ANOVA stand for?

11 What does the null hypothesis in a basic one-way ANOVA state?

12 Which type of data is commonly analyzed using a chi-square test?

13 A chi-square test of independence examines whether two categorical variables are what?

14 How does statistics support data science?

15 What symbol commonly represents the significance level?

16 Which two statements are directly compared in hypothesis testing?

17 Which everyday term best describes a Type 1 error?

18 Which everyday term best describes a Type 2 error?

19 Which p-value provides stronger evidence against the null hypothesis?

20 What does the null hypothesis in a chi-square test of independence usually state?

21 A data scientist measures the prediction latency of the same 30 servers before and after an optimization. Which test is most appropriate for comparing the mean latencies?

22 An online retailer tests whether a redesigned page changes the conversion rate from its current value of 8%. Which null hypothesis is appropriate?

23 A company will adopt a new recommendation algorithm only if it increases mean revenue above the current value of per user. Which alternative hypothesis should be used?

24 A hypothesis test produces a p-value of with significance level . What is the appropriate decision?

25 In a fraud-detection test, states that a transaction is legitimate. What is a Type I error?

26 A medical screening study uses : the patient does not have the condition. Which outcome represents a Type II error?

27 A data scientist wants to reduce the probability of a Type II error while keeping fixed. Which change is generally most effective?

28 A model comparison produces a p-value of . Which interpretation is correct?

29 A test returns . At which significance levels would the result be statistically significant?

30 A data scientist wants to compare mean customer spending across four membership tiers. Which test is the most appropriate initial analysis?

31 Which set of conditions best matches the standard assumptions of a one-way ANOVA?

32 An ANOVA comparing five model configurations is statistically significant. What should the data scientist do next to identify which means differ?

33 A researcher examines whether preferred device type (mobile, tablet, desktop) is associated with subscription status (free, paid). Which test is appropriate?

34 In a contingency table, a row total is 120, a column total is 50, and the grand total is 200. What is the expected count for their intersecting cell?

35 A die is rolled 120 times to determine whether its outcomes follow a uniform distribution. Which statistical test should be used?

36 What are the degrees of freedom for a chi-square test of independence using a contingency table?

37 A machine-learning model has 92% validation accuracy, while another has 91.8%. Why should a data scientist perform a statistical comparison?

38 A team independently tests 10 model features and wants a family-wise significance level of 0.05 using the Bonferroni correction. What threshold should each test use?

39 With a very large dataset, a new model reduces mean error by 0.001 units and produces . What is the best conclusion?

40 In a one-way ANOVA, what does a large -statistic generally indicate?

41 A researcher observes a symmetric test statistic and chooses the one-sided alternative only after seeing whether is positive or negative. They then reject whenever the selected one-sided p-value is below . Under , what is the actual Type I error rate?

42 For a composite null hypothesis , which p-value construction most directly guarantees that a level- test controls Type I error for every ?

43 To establish that a mean difference is practically equivalent to zero within a margin , which hypotheses are appropriate for the two one-sided tests procedure?

44 Twenty independent parameters each have a pointwise confidence interval. If all model assumptions hold, what is the probability that all 20 intervals simultaneously contain their parameters?

45 For a fixed nonzero effect size and correctly specified model, sample size is increased while the test threshold is recalibrated to keep . What generally happens?

46 A data scientist performs 20 independent hypothesis tests, each at significance level , and every null hypothesis is true. What is the probability of at least one Type I error?

47 A valid test produces . Which interpretation is correct?

48 Under , a one-sided test rejects for unusually large . If is observed, what is the exact p-value?

49 In a balanced ANOVA, treatment B exceeds treatment A by units at the low level of a second factor, but treatment B is units below treatment A at the high level. Which conclusion is most defensible?

50 Three groups each contain four observations. Their sample means are , , and , while the pooled within-group sum of squares is . What is the one-way ANOVA statistic ?

51 A study records five repeated measurements from each participant but analyzes all measurements using ordinary one-way ANOVA as if they came from different people. With positive within-participant correlation, what is the main inferential risk?

52 A one-way comparison has strongly unequal group variances and unequal sample sizes, with the largest variance occurring in the smallest group. Which omnibus procedure is generally most appropriate?

53 A chi-square goodness-of-fit test uses six categories. Two distribution parameters are estimated from the same observations before expected counts are calculated. What are the test's degrees of freedom?

54 A table has observed counts . What is Pearson's chi-square statistic without continuity correction?

55 Binary outcomes are measured on the same individuals before and after an intervention. Which test appropriately assesses marginal change while accounting for pairing?

56 A feature-selection algorithm is run once on the complete labeled dataset, after which cross-validation evaluates a model using only the selected features. Why is the estimated performance generally optimistic?

57 Suppose outcomes are missing at random conditional on observed covariates , and every observation has a positive response probability. Which method can consistently estimate the population outcome mean if its required model is correctly specified?

58 Five ordered p-values are . Using the Benjamini–Hochberg procedure with false discovery rate , how many hypotheses are rejected?

59 For four equally sized groups, which pair of contrasts is orthogonal?

60 An aggregated chi-square test shows a strong association between treatment and recovery, but the association largely disappears within every hospital. Hospital is related to both treatment assignment and recovery. What is the best next analysis?