Chapter 10

In one-way ANOVA, between-treatments variability is based on the variability ______. within each sample between sample means between population means

between sample means

Independent random samples are 1. the same samples at 2 different times. 2. completely unrelated to one another. 3. matched to each other in a particular way.

2. completely unrelated to one another.

For a given set of df1 and df2, what happens to the F values as α decreases? F approaches 0. F increases. F stays the same. F decreases

F increases.

True or false: A one-way analysis of variance (ANOVA) is used to test for equality of two population variances. True False

False

Which of the following pairs of hypotheses is used to test if the mean of Population 1 is smaller than the mean of Population 2 when using independent random sampling? H0: μ1 - μ2 ≤ 0 versus HA: μ1 - μ2 > 0 H0: μD ≤ 0 versus HA: μD > 0 H0: μD ≥ 0 versus HA: μD < 0 H0: μ1 - μ2 ≥ 0 versus HA: μ1 - μ2 < 0

H0: μ1 - μ2 ≥ 0 versus HA: μ1 - μ2 < 0

A one-way ANOVA test is based on the ______ distribution. χ2 z tdf F

F

In order to determine if there is a difference between the means of three or more populations, we use ______. a chi-square test of independence analysis of variance a goodness-of-fit test histograms or box plots.

analysis of variance

If we reject the null hypothesis H0: μ1=μ2=μ3 when conducting an ANOVA, we conclude that Only the populations with the largest and smallest sample means are different. all population means are equal. at least one population mean is different. all population means are different.

at least one population mean is different.

The degrees of freedom for the between-treatments variance is c n n - 1 c - 1

c - 1

What items are needed to describe a particular value of the F distribution? Select all that apply. μ2 df1 μ1 df2 α

df1 df2 α

In one-way ANOVA, two independent estimates of the common population variance σ2 are estimated. These estimates are commonly referred to as ______. biased variability and unbiased variability correlated variability and uncorrelated variability Type I variability and Type II variability between-treatments variability and within-treatments variability

between-treatments variability and within-treatments variability

When examining the difference between two population means, if the populations cannot be assumed normal, then (XX1 - XX2) is approximately normal if n1 ≥ 30 or n2 ≥ 30. n1 ≥ 30 and n2 ≥ 30. n1 ≥ 5 and n2 ≥ 5. n1p ≥ 5 and n2 p ≥ 5.

n1 ≥ 30 and n2 ≥ 30.

The notation Fα,(df1,df2) represents a value such that the area in the right tail of the distribution is α/2. left tail of the distribution is α. left tail of the distribution is α/2. right tail of the distribution is α.

right tail of the distribution is α.

For a given α level, what happens to the F values as df1 and df2 increase? F stays the same. F approaches 0. F decreases F increases.

F decreases

Which of the following are true about the test statistic for a one-way ANOVA test? Select all that apply. It is calculated by MSTR/MSE. df2 is found by subtracting 1 from the total number of observations. df1 is found by subtracting 1 from then number of populations.

It is calculated by MSTR/MSE. df1 is found by subtracting 1 from then number of populations.

Which one of the following is true about the shape of the F distribution? Its values range from 0 to -∝. It is bell-shaped and it becomes skewed as the degrees of freedom increases. It is skewed right and approaches the normal distribution as the degrees of freedom increases. It is skewed right or left, depending on the degrees of freedom.

It is skewed right and approaches the normal distribution as the degrees of freedom increases.

The alternative hypothesis HA in one-way ANOVA is All means are different. Not all population means are equal. All means are equal.

Not all population means are equal.

Which of the following is NOT an assumption for performing a one-way ANOVA? The population correlation coefficients indicate a strong linear relationship. The population standard deviations are unknown but assumed equal. The populations are normally distributed. The samples are selected independently.

The population correlation coefficients indicate a strong linear relationship.

When the population variances are known, which distribution does the test statistic follow? The t-distribution with the n-1 degrees of freedom. The z-distribution with n-1 degrees of freedom. The z-distribution. The t-distribution with n1 + n2 -2 degrees of freedom.

The z-distribution.

In one-way ANOVA, within-treatments variability is based on the sum of all observations in the data set divided by the total number of observations. a weighted sum of the sample variances of each treatment. a weighted sum of squared differences between the sample means and the grand mean.

a weighted sum of the sample variances of each treatment.

The hypotheses H0: μ1 - μ2 ≥ d0 versus HA: μ1 - μ2 < d0 indicate a left-tailed test. right-tailed test. two-tailed test.

left-tailed test.

A one-way analysis of variance (ANOVA) test compares population ______ based on one categorical variable or factor. variances standard deviations proportions means

means

The degrees of freedom for the within-treatments variance is nT - 1 c - nT nT - c c - 1

nT - c

In a one-way ANOVA test, if the amount of variability between treatments is significantly greater than the amount of variability within treatments, then we do not reject the null hypothesis of equal population means. reject the alternative hypothesis of at least one population mean being different. reject the null hypothesis of equal population means.

reject the null hypothesis of equal population means.

The one-way ANOVA test is always a right-tailed test. two-sided test. left-tailed test.

right-tailed test.

In comparing c population means, the ANOVA test assumes: the populations are skewed right. the population variances are known. the population variances are equal. the sample matched pairs.

the population variances are equal.

In a ANOVA test, we compute the grand mean by calculating: a weighted sum of the sample variances of each treatment. the sum of all the observations and then dividing by the total number of observations. a weighted sum of squared differences between the sample means and the grand mean.

the sum of all the observations and then dividing by the total number of observations.

In one-way ANOVA, within-treatments variability is based on the variability between sample medians. variability within each sample. variability between sample means.

variability within each sample.

True or false: If the populations are normally distributed, the z distribution is used to conduct an ANOVA test. True False

False

The competing hypotheses for a one-way ANOVA test that compares the means of three populations are defined as H0: μ1 = μ2 = μ3 HA: Not all population means are equal H0: μ1 ≠ μ2 ≠ μ3 HA: μ1 = μ2 = μ3 H0: μ1 = μ2 = μ3 HA: All population means are different H0: μ1 = μ2 = μ3 HA: μ1 ≠ μ2 ≠ μ3

H0: μ1 = μ2 = μ3 HA: Not all population means are equal

Suppose that you want to perform a test to compare the mean lifetime of two brands of batteries. One person purchases 10 Brand A batteries from a store and another person purchases 12 Brand B batteries from another store. What type of sampling is required for this test? Dependent sampling using before/after data Independent random samples Dependent sampling using matched pairs

Independent random samples

Which of the following are true about the F distribution? Select all that apply. Like the t distribution, the F distribution is characterized by a family of distributions. The F distribution is a negatively skewed distribution. Like the t distribution, it's value ranges from -∝ to ∝. It is like the t distribution in that it is based on degrees of freedom.

Like the t distribution, the F distribution is characterized by a family of distributions. It is like the t distribution in that it is based on degrees of freedom.

Select all that apply Which of the following is a scenario that exists when constructing a confidence interval for the difference in population means? The population variances are known. The population variances are unknown and assumed unequal. The sample medians are known to estimate the difference in population means. The population variances are unknown and assumed equal.

The population variances are known. The population variances are unknown and assumed unequal. The population variances are unknown and assumed equal.

We use ANOVA to determine ______. if differences exist between the means of three or more populations if differences exist between two population variances. if differences exist between two sample variances. if differences exist between two population proportions

if differences exist between the means of three or more populations

If we fail to reject the null hypothesis H0: μ1=μ2=μ3 when conducting an ANOVA, we conclude that at least one population mean is different from the others. none of the population means are equal. insufficient evidence exists to prove a difference in population means.

insufficient evidence exists to prove a difference in population means.

When comparing two population means, their hypothesized difference must be negative. must be zero. may assume any value. must be positive.

may assume any value.

Statistical inference concerning the difference in population means is based on the condition that the sampling distribution of (XX1 - XX2) follows a(n) ______ distribution. unknown binomial tdf normal

normal

When constructing a confidence interval for the difference between two population means, the margin of error equals the point estimate multiplied by zα/2 or tα/2,df. the margin of error multiplied by zα/2 or tα/2,df. zα/2 or tα/2,df. the standard error multiplied by zα/2 or tα/2,df.

the standard error multiplied by zα/2 or tα/2,df.

In one-way ANOVA, the independent estimates of the common population variance σ2 are based on which of the following? Select all that apply. difference in sample proportions. differences in sample medians. variability within each sample. variability between sample means

variability within each sample. variability between sample means

In most applications, the hypothesized difference between two population means is _____. negative positive one zero

zero