Practice Quiz-Lecture 7

Question 1

In the car example, the variable tire brand can be summarized using

Answer 1

Frequency or relative frequency

Question 1

Suppose the mean, median and mode of the mileage of cars using Apollo tires are 34,799 miles, 34,763 miles and 34,774 miles, respectively. What might be a plausible distribution for mileage

Answer 1

normal

Question 2

We can visualize the sample distribution of car mileage using a

Answer 2

histogram

Question 3

In a sample of 15 cars using Apollo tires, the average mileage was 34,799 miles. This average is an estimate of

Answer 3

the population mean of car mileage with Apollo tires

Question 4

To compare average mileage of Apollo versus Bridgestone tires using 15 cars using Apollo tires and 15 using Bridgestone tires with mileage having a right skewed distribution, we can use a

Answer 4

None of the above

Question 5

When testing whether the average mileage of cars using Apollo tires is equal to 35,000 miles using a sample of 15 cars, the sampling distribution of the test statistic is

Answer 5

t with 14 degrees of freedom

Question 6

When testing 7 null versus alternative hypotheses, family wise error rate is

Answer 6

Probability of rejecting at least one null hypothesis when all of them are true

Question 7

Answer true or false: Analysis of variance is an extension of paired t test

Answer 7

False

Question 8

Answer true or false: Analysis of variance is an extension of two-group t test

Answer 8

True

Question 9

Answer true or false: Analysis of variance tests the hypothesis that the means of a sample are the same across multiple categories of a categorical variable

Answer 9

False
-Correct: It compares the mean of a population, not sample

Question 10

When the categorical variable has just two categories, an Analysis of variance that compares the population means of a continuous variable between the two categories is equivalent to

Answer 10

Two group t test with the assumption of equal population variances

Question 11

Answer true or false: Total variation is the variance of the continuous variable of all the samples, regardless of which categories they fall into

Answer 11

True

Question 12

Analysis of variance partitions total variance into

Answer 12

Variation explained by the categorical explanatory variable and variance not explained by the explanatory variable

Question 13

Answer true or false: Between group variation characterizes the distance between population means

Answer 13

True

Question 14

Answer true or false: Within group variation characterizes the variance of the continuous variable within each category of the explanatory variable

Answer 14

True

Question 15

Answer true or false: When the distance between means is larger than within group variation, we are likely to reject the null hypothesis that all the population means are the same

Answer 15

True

Question 16

Sum of squares between groups represents

Answer 16

Distance between group-specific means and the overall mean of the continuous response

Question 17

Sum of squares within groups represents

Answer 17

Variance of the continuous response within each group

Question 18

The between group variation or mean square between is

Answer 18

Sum of squares between groups divided by the number of groups minus 1

Question 19

The test statistic under analysis of variance is given by

Answer 19

F = mean square between divided by mean square within

Question 20

The sampling distribution of the F statistic when there are C groups and N samples is

Answer 20

F distribution with C-1, N-C degrees of freedom

Question 21

When conducting an analysis of variance with 5 groups and 20 individuals per group, the degrees of freedom for between sum of squares is ______________

Answer 21

4

Question 22

When conducting an analysis of variance with 5 groups and 20 individuals per group, the degrees of freedom for within sum of squares is ___________ (give a number, not the notation or formula).

Answer 22

95

Question 23

Which of the following correctly represents the property of the F distribution

Answer 23

Mean > Median > Mode

Question 24

Answer true or false: The continuous response is assumed to have a normal distribution when analyzing data with ANOVA. However, ANOVA is robust to (i.e., ANOVA is not affected by) failure of this assumption

Answer 24

True

Question 25

Answer true or false: The population distributions of the continuous response in each category of the categorical variable are assumed to have the same variance

Answer 25

True

Question 26

Even when the population distributions do not have the same variance, it is okay to use ANOVA when

Answer 26

The sample size is the same in each category of the categorical variable

Question 27

When conducting 6 hypothesis tests by controlling the family wise error rate at 0.05 level, the type I error of each test will be

Answer 27

less than 0.05

Question 28

Answer true or false: ANOVA can be used to compare the population means of multiple groups when the samples are not independent

Answer 28

False