Unit 12: Hypothesis Testing - Practice Quiz

1 What is a statistical hypothesis?

2 What does the null hypothesis, , usually state?

3 What does the alternative hypothesis, , generally represent?

4 Which hypothesis is tested directly in a standard hypothesis test?

5 Which alternative hypothesis represents a two-tailed test for a population mean?

6 Which alternative hypothesis represents a right-tailed test?

7 What is normally the first step in hypothesis testing?

8 What does the significance level represent?

9 A significance level of is equal to what percentage?

10 What is a p-value?

11 What decision is usually made when the p-value is less than ?

12 What decision is usually made when the p-value is greater than ?

13 What is a Type I error?

14 What is a Type II error?

15 What is the purpose of a test statistic?

16 What is the critical region of a hypothesis test?

17 A manufacturer tests whether the mean bottle fill is mL. What is an appropriate null hypothesis?

18 A company tests whether a new advertisement increases average sales. Which test direction is appropriate?

19 How can hypothesis testing help a business evaluate employee training?

20 A quality manager tests whether a new process lowers the defect rate. What business decision can the test support?

21 Which statement is a statistical hypothesis?

22 A bottling company claims that its machines fill bottles with a mean of mL. Which null hypothesis represents this claim?

23 A retailer wants to determine whether a new layout increases mean daily sales above the previous mean of . What is the appropriate alternative hypothesis?

24 Which pair of hypotheses correctly tests whether a population proportion differs from ?

25 Why are the null and alternative hypotheses required to be mutually exclusive?

26 A population has known standard deviation . For , the sample mean is , and . What is the test statistic?

27 For versus , a test produces . At , the right-tail critical value is . What decision should be made?

28 A hypothesis test gives a p-value of . What is the correct decision at ?

29 A quality manager rejects : "The defect rate is no greater than " when the true defect rate is actually no greater than . What error occurred?

30 A bank fails to detect that the mean transaction time has increased when it actually has increased. Which error has occurred?

31 If the significance level is reduced from to while all other conditions remain unchanged, what generally happens?

32 A confidence interval for a difference in population means is . What conclusion follows for a two-tailed test of at ?

33 Historically, of customers cancel a subscription. In a sample of customers, cancel. For versus , which test statistic is closest?

34 A one-sample t-test is conducted using a random sample of observations. How many degrees of freedom are used?

35 Which change will generally increase the power of a hypothesis test when the effect size and significance level remain fixed?

36 A company compares customer spending before and after the same customers join a loyalty program. Which procedure is most appropriate?

37 An online retailer randomly assigns visitors to two page designs and compares their purchase proportions. Which test best evaluates whether conversion rates differ?

38 A manufacturer wants to determine whether defect status is associated with the supplier used. Both variables are categorical. Which test is appropriate?

39 A new advertisement produces a p-value of when testing whether mean weekly sales increased. The company selected before collecting data. What should it conclude?

40 A very large sample shows that a pricing change increases mean profit per transaction by with p-value below . What should management examine before implementation?

41 Which pair correctly classifies the hypotheses and ?

42 A manufacturer will adopt a process only if evidence shows that its mean defect rate is below the current benchmark . Which formulation places the burden of proof appropriately?

43 For testing against , why is the Type I error probability commonly calibrated at the boundary ?

44 A population has known standard deviation . For , the sample mean is . Testing against at , which conclusion is correct?

45 A symmetric test statistic produces an observed value . Under , . What is the two-sided -value when testing departure in either direction?

46 A one-sided -test of a mean uses . The standard deviation is , and the test should have power to detect an increase of . Using and , what minimum sample size is required?

47 A valid confidence interval for is . What follows for the corresponding two-sided test of at ?

48 Ten related null hypotheses are tested, and arbitrary dependence among their test statistics is possible. Which per-test threshold guarantees family-wise error rate at most by the Bonferroni method?

49 A company records each employee's productivity before and after introducing software. Measurements within an employee are strongly correlated. Which test most directly uses this design when normality of individual differences is plausible?

50 Two independent groups have unequal variances and unequal sample sizes. The observations are approximately normal. Which procedure best tests equality of population means without assuming equal variances?

51 In an A/B experiment, variant A has conversions among users and variant B has among . For versus , which result is closest for the pooled two-proportion -test?

52 A study reports for a correctly specified test. Which interpretation is valid?

53 An analyst repeatedly checks an ordinary fixed-sample -value after every new observation and stops when . No sequential correction was planned. What is the principal consequence?

54 Let denote the mean outcome for a new product minus that for a standard product, where larger is better. With noninferiority margin , which hypotheses test whether the new product is not worse by more than ?

55 An A/B test estimates an average revenue increase of per user with a confidence interval . Deployment costs require an increase of at least per user. Which conclusion is best?

56 A fraud screen flags of fraudulent transactions and of legitimate transactions. If of transactions are fraudulent, approximately what proportion of flagged transactions are actually fraudulent?

57 A retailer tests against , where is mean weekly demand. It increases inventory only after rejecting . In this setting, what is a Type II error?

58 A firm evaluates a regional advertising campaign using treated and untreated regions before and after launch. In a difference-in-differences regression, which hypothesis directly tests the campaign's average effect under parallel trends?

59 A marketing experiment randomizes treatment by store but analyzes thousands of customer purchases as independent observations. What is the most likely inferential problem?

60 A company tests five customer segments and plans to advertise success if any segment has . Assuming independent true nulls, what is the probability of at least one false rejection?