lesson questions 8.1

What is the ANOVA method used for?

To determine to reject the null hypothesis, or not.

To find out if three (or more) population means are equal.

To determine the relationship between three (or more) variables.

To find out if three (or more) population variances are equal.

To find out if three (or more) population means are equal

In the ANOVA table, how many hypothesis tests are there / what approach is used to make conclusion(s)?

One hypothesis test / The critical value approach.

One hypothesis test / The p-value approach.

A hypothesis test for each population / The p-value approach.

No hypothesis test(s) / No approach is used.

One hypothesis test / The p-value approach

In the ANOVA table, what is the null hypothesis / the alternative hypothesis?

Populations means are zero / Population means are not zero.

Populations means are equal / Population means are not equal.

Populations means are not equal / Population means are equal.

Populations variances are equal / Population variances are not equal.

Populations means are equal / Population means are not equal

In the ANOVA method, what is the main reason why several independent two-sample t-tests are not used to answer the question about the population means?

Because the F-test was invented before the t-test.

Because of a loss of control over the Type-I error rate (α).

Because independent two-sample t-tests cannot answer this question.

Because this approach involves a lot more work.

Because of a loss of control over the Type-I error rate (α)

Why does the ANOVA table take the approach to analyze variances to get information about population means?

This approach is simpler requiring only the variances and n (s2/n), and not the averages.

Standardized variances are easier to use in a t-test.

Equal variances imply equal population means.

This approach requires only one hypothesis test, thus controlling α.

This approach requires only one hypothesis test, thus controlling α

The ANOVA Fraction is the basis of the ANOVA table. What is the basis for the ANOVA Fraction?

The sampling distribution of the sample average.

The relationship between the sample variance and the population variance.

The sampling distribution of the sample variance.

The relationship between the standard deviation and the variance.

The sampling distribution of the sample average

In the ANOVA table, how is the Theoretical Variance calculated?

Calculating the sample variance of the three (or more) sample averages (s2¯x).

Pooling the sample variances and dividing by the count (s2p/n).

Calculating the sum-of-squares and dividing by the degrees of freedom (sosp/n−1).

Using an F-transformation to convert the sample variance (s2) into the Theoretical Variance (s2p/n).

Pooling the sample variances and dividing by the count (𝑠2𝑝/𝑛)

In the ANOVA table, how is the Actual Variance calculated?

Using an F-transformation to convert the sample variance (s2) into the Theoretical Variance (s2p/n).

Pooling the sample variances and dividing by the count (s2p/n).

Calculating the sum-of-squares and dividing by the degrees of freedom (sosp/n−1).

Calculating the sample variance of the three (or more) sample averages (s2¯x).

Calculating the sample variance of the three (or more) sample averages (𝑠2𝑥¯)

In the ANOVA table, what is the result when the values of all three (or more) population means are not equal?

The Actual Variance has the same mathematical sign as the Theoretical Variance.

The Actual Variance is larger than the Theoretical Variance.

The Actual Variance is close in size to the Theoretical Variance.

The Actual Variance is exactly equal to the Theoretical variance.

The Actual Variance is larger than the Theoretical Variance

In the ANOVA Table, what concept of testing does it follow for analyzing population means?

Several specific hypothesis tests of all pairs of population means.

An overall hypothesis test of all population means.

Comparing the confidence intervals for each population mean.

Calculating one confidence interval for all populations and see if it contains all sample averages.

An overall hypothesis test of all population means

Please select two choices that are the components of the ANOVA method?

Tukey Table

Levene's Table.

Sum-of-Squares Table.

ANOVA Table.

ANOVA Table

Tukey Table

In an ANOVA dataset, how are the data values arranged in the wide view / in the long view?

By importance of the variables / By rank of the variables.

By populations / By variables.

By order of the variables / By order of the data values.

By variables / By populations.

By populations / By variables

In the long view of an ANOVA dataset, what information is in the Response Variable / in the Factor Variable?

The measured data values / The names of the populations.

The values of the response variable / The values of the predictor variable.

A measured response / A controlled stimulus.

The measured data values / The appropriate multiplier.

The measured data values / The names of the populations

In an ANOVA data set, how many levels are there in the Factor Variable?

One for each population.

Up to three.

No levels.

Less than the number of data values.

One for each population

In the ANOVA method, select each choice that is an assumption of this method?

Each individual is selected randomly.

The population variances are equal.

All individuals are independent of each other.

The data values in each population have the normal shape.

Each individual is selected randomly

The population variances are equal

What information does the ANOVA table NOT give when the null hypothesis is rejected?

Which population means are equal.

How the population means are not equal.

That none of the population means are equal.

That all the population means are equal.

How the population means are not equal

In the Tukey Table, what concept of testing does it follow for analyzing population means?

Calculating one confidence interval for all populations and see if it contains all sample averages.

Several hypothesis tests for all pairs of population means.

An overall hypothesis test of all population means.

Comparing the confidence intervals for each population mean.

Several hypothesis tests for all pairs of population means

In the ANOVA table, what is the result when the value of all three (or more) population means are equal?

The Actual Variance is larger than the Theoretical Variance.

The Actual Variance has the same mathematical sign as the Theoretical Variance.

The Actual Variance is close in size to the Theoretical Variance.

The Actual Variance is exactly equal to the Theoretical variance.

The Actual Variance is close in size to the Theoretical Variance

In the ANOVA table, what information does the Theoretical Variance give?

The calculated spread of the sample averages coming from one population.

The expected spread of the sample averages coming from one population.

The expected spread of the sample variances coming from one population.

Two of these other answers.

The expected spread of the sample averages coming from one population

In the ANOVA table, what information does the Actual Variance give?

The calculated spread of the sample averages.

The calculated spread of the sample variances.

The calculated spread of the population means.

The calculated spread of the data values.

The calculated spread of the sample averages

In the ANOVA table, how are these two special variances actually analyzed?

By multiplying to see if the resulting value is positive.

By converting into F-values and comparing.

By dividing to see if the resulting value is close to one.

By subtracting to see if the resulting value is close to zero.

By dividing to see if the resulting value is close to one

In the long view of an ANOVA dataset, what type of data is in the factor variable / in the response variable?

Discrete data / Qualitative data.

Qualitative data / Continuous data.

Continuous data / Continuous data.

Continuous data / Qualitative data.

Qualitative data / Continuous data

In an ANOVA dataset, how many levels are in the factor variable if it contains four values: freshman, sophomore, junior, and senior?

Two of these other answers.

Four levels.

One level for a one-way ANOVA.

One level for each population.

Two of these other answers

How many factor variables are in a One-Way ANOVA?

One factor variable for each categorical variable in the dataset.

Two of these other answers.

One factor variable for a one-way ANOVA.

One factor variable for each population.

One factor variable for a one-way ANOVA

In the ANOVA table, there are four assumptions to be met. What is the focus of the first two assumptions / the last two assumptions?

Concerns random selection / Concerns normality.

Concerns the data values / Concerns the populations.

Concerns the Theoretical variance / Concerns the Actual variance

Concerns proper data values / Concerns a proper dataset.

Concerns the data values / Concerns the populations

In the ANOVA table, what does the assumption of Normality mean?

The shape of each population is normal.

The shape of each data value is normal.

The shape of the response variable is normal.

The shape of the factor variable is normal.

The shape of each population is normal

In the ANOVA table, what does the assumption of Equal Variance mean?

All populations have the same variance.

The mathematical sign in the alternative hypothesis is not equal (≠).

All data values have the same variance.

The response variable and the factor variable have the same variance.

All populations have the same variance

In the ANOVA table, what is the ANOVA fraction?

Fraction=Actual Variance/Theoretical Variance .

Fraction=Theoretical Variance/Actual Variance .

Fraction=Response Variance/Levels Variance .

Fraction=Response Variance/Factor Variance .

Fraction=𝐴𝑐𝑡𝑢𝑎𝑙 Variance/𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 Variance