Chapter 10 assign.

Which of the following methods below are types of matched-pairs experiments? Select all that apply.

"Before" and "after" studies A pairing of observations in each sample by some common characteristic

Regardless of the distribution used, the numerator of test statistics for difference between population mean is

(X1 - X2) - d0

The assumption for statistical inference for the mean difference using matched-pairs sampling requires either normality regarding the paired differences D = X1 - X2 or that the sample size n be at least

30

A one-way ANOVA test is based on the ______ distribution.

F

For a given set of df1 and df2, what happens to the F values as α decreases?

F increases.

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

False

A researcher claims that the average customer amount spent on groceries is more in Neighborhood 1 than in Neighborhood 2. The competing hypotheses for this claim are:

H0: μ1 - μ2 ≤ 0 versus HA: μ1 - μ2 > 0

What is formula for the mean square error (MSE)?

Sum of squares / degrees of freedom

When the population variances are unknown and assumed equal, we calculate a pooled estimate of the population variance. What are the weights that are used to calculate the pooled variance?

The degrees of freedom

When the population variances are known, which distribution does the test statistic follow?

The z-distribution.

In order to determine if there is a difference between the means of three or more populations, we use ______.

analysis of variance

If we reject the null hypothesis H0: μ1=μ2=μ3 when conducting an ANOVA, we conclude that

at least one population mean is different.

The degrees of freedom for the between-treatments variance is

c - 1

Independent random samples are

completely unrelated to one another.

The confidence interval for the mean difference μD in paired samples is

dd ± tα/2,df sdn

Matched-pairs sampling is an example of

dependent sampling

A confidence interval for the mean difference μD follows the general format of a point estimate ±

margin of error.

Performing a one-way ANOVA test, instead of performing a series of two-sample t tests, ______ the risk of incorrectly rejecting the null hypothesis.

reduces

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

reject the null hypothesis of equal population means.

The one-way ANOVA test is always a

right tailed test

The hypotheses H0: μ1 - μ2 ≤ d0 versus HA: μ1 - μ2 > d0 indicate a

right-tailed test.

A one-way ANOVA test is better than using a series of two-sample t tests because conducting a

series of two-sample t tests inflates the risk of committing a Type I error.

If you conduct a matched-pairs hypothesis test about the mean difference μD, then you calculate the value of the test statistic as

simple one tdf = d-d0sD/n

In comparing c population means, the ANOVA test assumes

the population variances are equal.

A pooled estimate of the common variance between two populations is used when

the population variances are unknown, but assumed equal.

When constructing a confidence interval for the difference between two population means, the margin of error equals

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

We calculate a pooled estimate of the common variance by

using weighted averages of the sample variances.

In most applications, the hypothesized difference between two population means is _____.

zero

The parameter of interest for matched-pairs sampling is denoted as ______.

μD

Suppose the competing hypotheses for a test at the 5% significance level are H0: μD = 0 versus HA: μD ≠ 0. Which of the following would lead to rejecting the null?

The 95% confidence interval for μD that does not include 0.

In one-way ANOVA, between-treatments variability is based on the variability ______.

between sample means

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. It is like the t distribution in that it is based on degrees of freedom.

Statistical inference concerning the mean difference based on matched-pairs sampling requires one of two conditions. Select the two conditions.

The distribution of differences is normally distributed. The sample size n ≥ 30.

In one-way ANOVA, between-treatments variability is based on

a weighted sum of squared differences between the sample means and the grand mean.

In one-way ANOVA, within-treatments variability is based on

a weighted sum of the sample variances of each treatment.

In one-way ANOVA, two independent estimates of the common population variance σ2 are estimated. These estimates are commonly referred to as ______.

between-treatments variability and within-treatments variability

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

f

A specific type of dependent sampling when the samples are paired in some way is called

matched-pairs sampling.

For matched-pairs sampling, the parameter of interest is referred to as the

mean difference.

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

The alternative hypothesis HA in one-way ANOVA is

Not all population means are equal.

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 population variances are unknown and assumed equal.

When comparing two population means, their hypothesized difference

may assume any value.

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

means

When examining the difference between two population means, if the populations cannot be assumed normal, then (X1 - X2) is approximately normal if

n1 ≥ 30 and n2 ≥ 30.

Statistical inference concerning the difference in population means is based on the condition that the sampling distribution of (X1 - X2) follows a(n) ______ distribution.

normal

In one-way ANOVA, within-treatments variability is based on the

variability within each sample.

The confidence interval for the difference between two population means when the population standard deviations are unknown and assumed equal is

(x1 - x2) ± tα/2,dfsp2(1n1+1n2

The confidence interval for the difference between two population means when the samples are independent and the population standard deviations are knownis

(x1 - x2) ± zα/2 √σ12n1+σ22n2

Suppose a test of H0: μ1 = μ2 is being conducted at the 5% significance level. For which of the following 95% confidence intervals for μ1 - μ2 would the null be rejected?

-1.2 to -0.8

Which of the following are examples of matched-pairs experiments? Select all that apply.

A study of salaries for two cities is conducted by matching employees in the cities according to major and work experience. The same individuals are evaluated before and after a weight loss program.

Suppose that the competing hypotheses for a test are H0: μD = 0 versus HA: μD ≠ 0. A 95% confidence interval for the mean difference is calculated as [-1, 4]. At the 5% significance level, the correct conclusion to the hypothesis test is:

Do not reject H0; the mean difference does not significantly differ from zero.

For a matched-pairs test, the null and alternative hypotheses to test whether the mean difference μD differs from a given hypothesized value d0 are

H0: μD = d0 versus HA: μD ≠ d0 .

Which of the following would be an acceptable null hypothesis? Select all that apply.

H0: μD ≤ 5 H0: μD ≠ -2 H0: μD = 0

For a matched-pairs test, the null and alternative hypotheses for a right-tailed test concerning the mean difference μD are constructed as

H0: μD ≤ d0 versus HA: μD > d0.

A confidence interval could be used to test for a difference in population means. Under what conditions would the null be rejected? Select all that apply.

If the hypothetical difference, d0, is less than the lower value of the confidence interval. If the hypothetical difference, d0, is greater than the upper value of the confidence interval.

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?

Independent random samples

Which of the following is NOT an assumption for performing a one-way ANOVA?

The population correlation coefficients indicate a strong linear relationship.

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. df1 is found by subtracting 1 from then number of populations.

We use ANOVA to determine ______.

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

insufficient evidence exists to prove a difference in population means.

The notation Fα,(df1,df2) represents a value such that the area in the

right tail of the distribution is α.

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

Which one of the following is true about the shape of the F distribution?

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

When the population variances are unknown and assumed equal, what are the degrees of freedom?

n1 + n2 - 2

In one-way ANOVA, the independent estimates of the common population variance σ2 are based on which of the following? Select all that apply.

variability within each sample. variability between sample means

For a given α level, what happens to the F values as df1 and df2 increase?

F decreases

The test statistic for a one-way ANOVA test follows the

Fdf1,df2 distribution.

Which of the following is true about the test statistic for a hypothesis test about the mean difference μD?

It follows the t-distribution. It is valid only if the distribution of D is normal.

What items are needed to describe a particular value of the F distribution? Select all that apply.

df1 df2 α

Two or more random samples are considered independent

if the process that generates one sample is completely separate from the process that generates the other sample.

The competing hypotheses for a left-tailed matched-pairs test concerning the mean difference μD are constructed as

H0: μD ≥ d0; HA: μD < d0.

In a ANOVA test, we compute the grand mean by calculating

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