Deck 10: Hypothesis Testing Iii the Analysis of Variance

Question 1

ANOVA may be thought of as an extension of the ______________.________.

A) confidence interval estimation procedure
B) t test for the significance of the difference between two sample proportions
C) t test for the significance of the difference between two sample means
D) t test for the significance of the difference between two matched samples

Answer 1

C

Question 2

ANOVA proceeds by developing two separate estimates of the _________.

A) population mean.
B) population standard deviation.
C) population variance.
D) sample variance.

Answer 2

C

Question 3

The ANOVA test is most appropriate for dependent variables that are________.

A) discrete and ordinal.
B) discrete and continuous.
C) continuous and nominal.
D) continuous and interval-ratio.

Answer 3

D

Question 4

A useful computational shortcut for the ANOVA test is expressed as________.

A) SST = SSB/SSW
B) dfw = dfb + SST
C) SSW = SST - SSB
D) SSB = SSW - SST

Question 5

The quantity SSW measures the amount of variation________.

A) after subtracting the total variation (SST).
B) within the categories.
C) in the population.
D) assuming the null hypothesis is true.

Question 6

In the ANOVA test, the symbol 'dfb' refers to________.

A) the mean square estimate between.
B) degrees of freedom associated with SSB.
C) degrees forward beneath.
D) degrees of fullness, behind estimate.

Question 7

Which of the following is an assumption that must be made in Step 1 of the ANOVA test?

A) Independent random samples
B) Dependent random samples
C) Level of measurement is nominal
D) Stratified random samples

Question 8

The research hypothesis for the ANOVA test is________.

A) μ 1 μ 2 μ 3 μ N.
B) that at least one population mean is different.
C) SST = SSB = SSW.
D) that at least one of the sums of squares is different.

Question 9

The total sum of squares (SST) is found by subtracting the overall mean from __________ and squaring and summing the differences.

A) the category means
B) the category totals
C) each of the scores
D) the sum of squares between

Question 10

The degrees of freedom for the Sum of Squares Within (SSW) is based upon the________.

A) total number of cases.
B) difference between total number of cases and categories.
C) total number of categories.
D) sum of the total number of cases and categories.

Question 11

The sampling distribution for the ANOVA test is________.

A) the Z distribution.
B) the t distribution.
C) the F distribution.
D) None of the answer choices

Question 12

ANOVA is a one tailed test and we are concerned only with those outcomes in which there is more variance________.

A) within categories than between categories.
B) between categories than within categories.
C) within populations than samples.
D) within samples than populations.

Question 13

The ANOVA test is designed for dependent variables that have been measured at _______.

A) the interval-ratio level.
B) the nominal level.
C) the ordinal level.
D) any level of measurement.

Question 14

Which of the following correctly states the relationship between SST (the total sum of squares), SSB (the sum of squares between), and SSW (the sum of squares within)?

A) SST = SSB + SSW
B) SST = SSB - SSW
C) SSW = SSB + SST
D) SSB = SST - SSW

Question 15

The population variance is a measure of _________.

A) central tendency.
B) dispersion.
C) location.
D) degrees of freedom.

Question 16

The F ratio is equal to________.

A) SST - SSB.
B) the "mean square between" divided by the "mean square within."
C) the "mean square within" minus the "mean square between."
D) the total variance divided by the mean square between.

Question 17

To construct estimates of the population variance, we divide each sum of squares by its respective________.

A) degrees of freedom.
B) N.
C) category mean.
D) standard deviation.

Question 18

In the ANOVA test, the symbol 'dfw' refers to________.

A) the mean square estimate within.
B) degrees of freedom associated with SSW.
C) degrees forward without.
D) degrees of fullness, within estimate.

Question 19

For ANOVA, we construct two estimates of the population variance. These are called________.

A) the average estimates.
B) the standard estimates.
C) the within and total estimates.
D) the mean square estimates.

Question 20

The degrees of freedom for the Sum of Squares Between (SSB) is based upon the________.

A) total number of categories.
B) total number of cases.
C) difference between total number of cases and categories.
D) sum of the total number of cases and categories.

Question 21

Three different sections of the same Interstate highway, with roughly equal traffic volumes, have been patrolled by the State Police at different levels of intensity for the past six months. The posted speed limit is 55 and the speeds of a random sample of motorists have been registered for each of the three sections. Is there any statistically significant difference in the speeds? Use the five step model as a guide and write a sentence or two of interpretation for your results.

Question 22

The ANOVA test uses means and standard deviations to compare the amount of variation ______________ with the amount of variation ______________.

A) within categories, between categories
B) above categories, below categories
C) within sample means, between sample means
D) within sample standard deviations, between sample standard deviations

Question 23

A researcher is analyzing regional differences in family size. She has information on number of children for samples of families from four regions. Which of the following would be an appropriate statistical test?

A) t test for matched samples
B) t test for difference in means
C) ANOVA
D) Actually, none of the answer choices would work in this situation

Question 24

Analysis of Variance based upon the effect of a single variable upon another is a________.

A) Two-way ANOVA.
B) One-way ANOVA.
C) Multiple ANOVA.
D) None of these choices are correct.

Question 25

In the ANOVA test, degrees of freedom within (dfw) are equal to ______ and degrees of freedom between (dfb) are equal to (k - 1).

A) (N - k)
B) (k + 1)
C) (N + k)
D) (k - N)

Question 26

In the ANOVA test, degrees of freedom within (dfw) are equal to (N - k) and degrees of freedom between (dfb) are equal to ________.

A) (N - k)
B) (k - 1)
C) (N + k)
D) (k - N)

Question 27

A random sample of 15 families representing three social classes has been observed for the frequency with which the parents administer physical punishment to the children over a period of a week. Are the differences significant? Use the five step model as a guide and write a sentence or two of interpretation for your results.

Question 28

With the ANOVA test, the ___________ the difference between categories, relative to the differences within, the ________ likely that the null hypothesis will be rejected.

A) smaller, more
B) greater, more
C) smaller, less
D) b & c are both correct

Question 29

Stated generally, the null hypothesis for the ANOVA test is________.

A) μ 1 = μ 2 = μ 3 = ... = μ k
B) σ 1 = σ 2 = σ 3 = ... = σ k
C) SST = SSB = SSW
D) dfb = dfw

Question 30

One limitation of ANOVA is that, when the null hypothesis is rejected, the test________.

A) does not tell us which sample mean(s) is/are different.
B) tells us nothing about the standard deviations.
C) does not tell us which population variances are zero.
D) does not tell us which population variances are greater than zero.

Question 31

When we have an interval-ratio dependent variable and are comparing two groups, the appropriate test of significance is the ________. When we have an interval-ratio dependent variable and are comparing three or more groups, the appropriate test of significance is the ________.

A) t test, ANOVA
B) ANOVA, t test
C) chi square, ANOVA
D) t test, chi square

Question 32

In an ANOVA test, when the null hypothesis is rejected, we know that at least one of the means is significantly different from the others. In order to find out which mean(s) are significantly different, we must conduct a________.

A) t test.
B) post hoc test.
C) post mortem test.
D) chi square test.

Question 33

In the ANOVA test, if the null hypothesis is true________.

A) the sample standard deviations should be zero.
B) the sample means should be roughly equal in value.
C) the population means should be very different from each other.
D) alpha should be less than zero.

Question 34

In an ANOVA test, if MSB is significantly _____ than the MSW, we will ________.

A) less, reject the null hypothesis
B) greater, reject the null hypothesis
C) greater, fail to reject the null hypothesis
D) greater, recompute as this is mathematically impossible

Question 35

If we reject the null hypothesis in a test using analysis of variance, we are concluding that________.

A) the populations from which our samples come are different.
B) the variables are independent.
C) the population variances are the same.
D) the sample means are significantly different.

Question 36

A researcher has analyzed differences in average College Board scores for random samples of students from four different colleges. The obtained F score is 0.45. What can be concluded about the null hypothesis?

A) Nothing, more information is needed
B) Reject, the differences did not occur by random chance
C) Fail to reject, differences are not statistically significant
D) Fail to reject, differences are statistically significant

Question 37

In a test using ANOVA, the average ages of three different samples are 37.56, 37.57, 37.58. This pattern would be consistent with the assumption that the________.

A) null hypothesis is false.
B) null hypothesis is true.
C) research hypothesis is false.
D) sample standard deviations approach zero.