Practice Quiz-Lecture 7 Flashcards
In the car example, the variable tire brand can be summarized using
Frequency or relative frequency
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
normal
We can visualize the sample distribution of car mileage using a
histogram
In a sample of 15 cars using Apollo tires, the average mileage was 34,799 miles. This average is an estimate of
the population mean of car mileage with Apollo tires
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
None of the above
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
t with 14 degrees of freedom
When testing 7 null versus alternative hypotheses, family wise error rate is
Probability of rejecting at least one null hypothesis when all of them are true
Answer true or false: Analysis of variance is an extension of paired t test
False
Answer true or false: Analysis of variance is an extension of two-group t test
True
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
False
-Correct: It compares the mean of a population, not sample
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
Two group t test with the assumption of equal population variances
Answer true or false: Total variation is the variance of the continuous variable of all the samples, regardless of which categories they fall into
True
Analysis of variance partitions total variance into
Variation explained by the categorical explanatory variable and variance not explained by the explanatory variable
Answer true or false: Between group variation characterizes the distance between population means
True
Answer true or false: Within group variation characterizes the variance of the continuous variable within each category of the explanatory variable
True
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
True
Sum of squares between groups represents
Distance between group-specific means and the overall mean of the continuous response
Sum of squares within groups represents
Variance of the continuous response within each group
The between group variation or mean square between is
Sum of squares between groups divided by the number of groups minus 1
The test statistic under analysis of variance is given by
F = mean square between divided by mean square within
The sampling distribution of the F statistic when there are C groups and N samples is
F distribution with C-1, N-C degrees of freedom
When conducting an analysis of variance with 5 groups and 20 individuals per group, the degrees of freedom for between sum of squares is ______________
4
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).
95
Which of the following correctly represents the property of the F distribution
Mean > Median > Mode
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
True
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
True
Even when the population distributions do not have the same variance, it is okay to use ANOVA when
The sample size is the same in each category of the categorical variable
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
less than 0.05
Answer true or false: ANOVA can be used to compare the population means of multiple groups when the samples are not independent
False
