Unit 13: Tests of Significance - Practice Quiz

1 Which distribution is commonly used to test a population mean when the population standard deviation is known?

2 Who introduced Student's t-distribution under the pen name "Student"?

3 Student's t-distribution is especially useful when the sample size is small and which quantity is unknown?

4 What is the shape of Student's t-distribution?

5 How do the tails of a t-distribution compare with those of the standard normal distribution?

6 For a one-sample t-test based on observations, what are the degrees of freedom?

7 A critical value of marks the boundary between which two regions?

8 Which two quantities are needed to find a critical t-value from a table?

9 Which is a common application of the t-distribution?

10 In a test for a single mean, what does the null hypothesis usually state?

11 Which statistic is used for a one-sample t-test?

12 For a small-sample one-mean t-test, the population is generally assumed to be approximately what?

13 What does an independent two-sample t-test compare?

14 In a paired t-test, the analysis is performed on which values?

15 What is the usual null hypothesis for a test comparing two population means?

16 Fisher's Z-transformation is primarily applied to which statistic?

17 Which formula gives Fisher's transformation of a correlation coefficient ?

18 An F-statistic is generally formed as a ratio of what?

19 Which information is required to locate a critical F-value in an F-table?

20 Which statistical method commonly uses the F-distribution to compare several group means?

21 A random sample of observations is drawn from a normal population. The population variance is unknown, and the hypothesis concerns the population mean. Which test statistic is most appropriate?

22 Let be standard normal and be chi-square with degrees of freedom, independently. Which expression has Student's -distribution with degrees of freedom?

23 What is the variance of a -distributed random variable with degrees of freedom?

24 For a two-tailed -test with degrees of freedom and significance level , a table gives . What are the rejection boundaries?

25 A sample of observations has mean and standard deviation . Using , what is the confidence interval for the population mean?

26 A sample of items has and . To test , what is the value of the one-sample -statistic?

27 For against , a sample of gives and . If the upper critical value at is , what is the conclusion?

28 Two independent normal samples have and . Assuming equal variances, what is the pooled two-sample -statistic for testing ?

29 For matched pairs, the sample mean and standard deviation of the differences are and , respectively. What is the paired -statistic for testing a zero mean difference?

30 When comparing the means of two independent normal populations, in which situation is Welch's -test generally preferred over the pooled -test?

31 Fisher's transformation of a sample correlation is . What is the transformed value when ?

32 Two independent samples each have size and correlations and . Their Fisher-transformed values are and . What is the approximate -statistic for testing equality of the population correlations?

33 If and are independent chi-square variables with and degrees of freedom, respectively, which ratio follows an distribution?

34 An upper-tailed variance test has an observed statistic . If the upper critical value for degrees of freedom is , what decision should be made?

35 Suppose the upper critical value of is . Using the reciprocal property, what is the lower critical value of ?

36 Two independent samples have variances and . If the larger sample variance is placed in the numerator, what is the variance-ratio statistic?

37 In a one-way ANOVA, the mean square between groups is and the mean square within groups is . What is the test statistic?

38 Which statement correctly describes the general shape and support of an -distribution?

39 A population has known standard deviation . A sample of observations has mean . What is the -statistic for testing ?

40 Two independent populations have known standard deviations and . Samples with sizes and have means and . What is the two-sample -statistic for testing ?

41 A normal population is sampled with , , and . For testing against , suppose and , where subscripts denote upper-tail probabilities. Which conclusion is correct?

42 For , , and , test against at . Given , which statement correctly links the test and the corresponding one-sided confidence bound?

43 Ten matched pairs produce differences with and . For a two-sided test of , use and . What is the strongest justified conclusion?

44 Two independent normal samples have and . Without assuming equal variances, which Welch statistic and approximate degrees of freedom are correct for testing ?

45 Independent normal samples have and . Assuming equal population variances, which pooled test statistic is correct?

46 Consider three studies: I tests one normal-population mean with known variance; II compares two independent normal means with unknown, unequal variances; III compares two normal-population variances. Which sequence of reference distributions is appropriate?

47 Which statement is correct for a central t-distribution with degrees of freedom?

48 Let be normal with mean and variance . For , what is the exact distribution of when ?

49 Five two-sided confidence intervals for normal-population means are to have simultaneous coverage of at least using Bonferroni's method. Each interval has degrees of freedom. Which upper-tail t critical value should each interval use?

50 If has a central t-distribution with degrees of freedom, which F-based rejection rule is exactly equivalent to the two-sided level- rule ?

51 A one-sided Z test of against uses , known , and . Taking , what is the test's approximate power when the true mean is ?

52 Two independent populations have known standard deviations and . Samples give , , , and . For a two-sided Z test of equal means, which result is correct?

53 Independent normal samples have , , , and . If the variance-ratio statistic is defined as , which null distribution and observed value apply under ?

54 Let denote an upper-tail critical value. Given , what is the lower critical value for an variable?

55 A one-way ANOVA has four groups and total observations. The between-group and within-group sums of squares are and , respectively. Given , what conclusion follows?

56 A multiple regression with observations and predictors has . What is the overall F statistic for testing that all three slope coefficients are zero?

57 A reduced regression model has and error degrees of freedom. Adding two predictors gives and error degrees of freedom. What is the partial F statistic for the added predictors?

58 A sample of size has correlation . Test using Fisher's transformation and standard error . Which result is correct?

59 For and sample correlation , which interval is the approximate confidence interval for obtained by constructing an interval on the Fisher-Z scale and transforming back?

60 Two independent studies report from observations and from observations. Using Fisher transformations, what is the approximate statistic for testing equality of the population correlations?