Deck 9: Hypothesis Testing III: the Analysis of Variance

Question 1

A researcher is comparing random samples of white, black, and Hispanic Americans for differences in income, family size, and years of education. Which of the following tests of significance would be useful for all three dependent variables?

A) t test for small samples
B) t test for difference in means
C) ANOVA
D) the test for the significance of the difference between sample proportions

Answer 1

ANOVA

Question 2

What would be the most appropriate test of significance for research situations in which we have an interval-ratio dependent variable and an independent variable with three or more categories?

A) the t test
B) Chi square
C) ANOVA
D) the IQV

Answer 2

ANOVA

Question 3

We have rejected the null hypothesis in an ANOVA test. This means that the variation _________ the samples is significantly greater than the variation ________ the samples.

A) within … between
B) above … below
C) outside … inside
D) between … within

Answer 3

between … within

Question 4

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 5

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

Question 6

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 7

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 8

ANOVA proceeds by developing two separate estimates of the

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

Question 9

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 10

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 above would work in this situation

Question 11

The population variance is a measure of

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

Question 12

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) b & c are both correct

Question 13

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

Question 14

If we fail to reject the null hypothesis in a test using analysis of variance, we are concluding that

A) the populations from which our samples come are the same
B) the samples are dependent
C) the population variances are the different
D) the sample means are different

Question 15

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 16

In the ANOVA test, if the null hypothesis is false, the means of the different sample should be _____________ and the standard deviation of the different samples should be ____________ .

A) similar in value … large in value
B) close to zero … equal to their respective variances
C) very different … lower in value then the means
D) very different in value … relatively low in value

Question 17

Stated generally, the null hypothesis for the ANOVA test is

A) $\mu$ 1 = $\mu$ 2 = $\mu$ 3 = ... = $\mu$ k
B) $\sigma$ 1 = $\sigma$ 2 = $\sigma$ 3 = ... = $\sigma$ k
C) SST = SSB = SSW
D) dfb = dfw

Question 18

A null hypothesis that states "the population means are equal" would be appropriate for which of the following tests of significance?

A) chi square
B) tests of proportions
C) ANOVA
D) Fisher's Exact test

Question 19

ANOVA is appropriate for situations in which

A) only nominal level variables are involved
B) we are comparing more than two groups
C) bivariate tables are used to organize the data
D) there are fewer than two samples

Question 20

The null hypothesis for ANOVA states that

A) the variables are independent
B) the variables are related
C) the population means are equal
D) the population means are different

Question 21

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 22

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 23

The research hypothesis for the ANOVA test is

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

Question 24

In the ANOVA test, what assumption must be made with regard to the population variances?

A) they are equal
B) they are unequal
C) they are both less than zero
D) they are equal to each other and to zero

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

The total sum of squares (SST) is found by finding the sum of the squared _____ and then subtracting the mean-squared times ____ .

A) deviations … s
B) deviations … N
C) scores … N
D) scores … s

Question 27

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 28

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 29

The ANOVA test will tolerate some violation of the model assumptions as long as

A) sample size is quite small
B) sample sizes are roughly equal
C) at least one sample is greater than 50
D) there are more than 4 separate samples

Question 30

In the ANOVA test, if the null hypothesis is true, then

A) SSB should be at least twice as much as dfb
B) SSW should be much greater than SSB
C) the combined dfb and dfw should be much greater than the SST
D) the mean square between (MSB) and the mean square within (MSW) should be roughly equal in value

Question 31

In the ANOVA test, what assumption must be made about the shape of the population distribution?

A) the population distribution is normal in shape
B) the test is non-parametric, no assumption need be made about the population
C) population distribution is a bivariate table
D) the test is parametric, population distribution is assumed to not be normal

Question 32

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 33

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 34

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) simple random samples

Question 35

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 36

The F ratio is a ratio of _________ to _________ .

A) amount of variation between categories to the amount of variation within
B) amount of variation within categories to the amount of variation between
C) total variation to amount of variation between
D) total variation to amount of variation within

Question 37

The sampling distribution for the ANOVA test is

A) the Z distribution
B) the t distribution
C) the F distribution
D) None of the above

Question 38

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 39

The ANOVA test is most appropriate for dependent variables that are

A) ordinal
B) nominal
C) less than zero
D) interval-ratio

Question 40

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 41

In an ANOVA test, if MSB is significantly _____ than 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 42

Very large random samples of Catholics, Protestants, and people with no religious affiliation have been questioned about their opinions on capital punishment. On a ten point scale, the Protestants average 6.9, the Catholics averaged 7.0, and people with no religious affiliation averaged 7.1. These differences were tested by ANOVA and found to be statistically significant. What is the most reasonable conclusion?

A) This is a statistically significant and important difference
B) This difference may be statistically significant but it seems unimportant
C) This difference is due to random chance
D) The researcher should have used sample means rather than proportions in this situation

Question 43

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 44

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 null hypothesis, the differences did not occur by random chance
C) Fail to reject the null hypothesis, differences are not statistically significant
D) Fail to reject the null hypothesis, differences are statistically significant

Question 45

According to a study of weight loss cited in the text,

A) exercise helped to limit weight gain
B) those who exercised the most lost significantly more weight
C) women lost weight, men gained weight
D) all subjects lost weight, regardless of the amount of exercise

Question 46

One limitation of the ANOVA test is that it requires

A) nominal level dependent variables
B) ordinal level independent variables
C) very small samples
D) an interval-ratio dependent variable

Question 47

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 48

If our F (obtained) exceeds the F (critical), we

A) reject the null
B) accept the null
C) must recompute since this is mathematically impossible
D) reject the research hypothesis