ch 9 isds reading questions

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.

The normal distribution approximation for a binomial distribution is valid when

np ≥ 5 and n(1 - p) ≥ 5

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

The one-way ANOVA test is always a

right tailed test

We would conduct a hypothesis test to determine whether or not

sample evidence contradicts H0.

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

tdf = d−d0sD/n√

The p-value is calculated assuming the

the null hypothesis is true

The critical value of a hypothesis test is

the value that separates the rejection region from the non-rejection region.

When performing a hypothesis test on μ when σ is known, H0 can be rejected for which of the following cases? Select all that apply.

z > zα for a two-tailed test. z < zα for a left-tailed test. z < zα for a two-tailed test.

Regardless of the distribution used, the numerator is

(XX1 - XX2) - d0

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

at least one population mean is different.

For a given sample size n, α can only be reduced

at the expense of increasing β.

If the chosen significance level is α = 0.05, then there is a 5% chance of

rejecting a true null hypothesis.

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.

The proportion would be the appropriate descriptive measure when trying to estimate the

the percentage of students living off-campus.

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

variability within each sample.

For a hypothesis test concerning the population proportion p, the value of the test statistic is calculated as

z = p−p0 / p0(1−p0) ÷ n √

We do NOT reject the null hypothesis when the p-value is

≥ α.

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

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

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

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

df2 α df1

All of the following are approaches to implementing a hypothesis test EXCEPT:

the sample test

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

We can reject the null hypothesis when the

p-value < α.

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

F increases.

The confidence interval for the difference between two population means when the population standard deviations are unknown and cannot be assumed equal is

(xx1 - x2x2) ± tα/2,df √s12n1+s22n2

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

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a two-tailed test is (are):

-z0.05 and z0.05

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.

The significance level is the allowed probability of making

a Type I error.

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

Fdf1,df2 distribution.

The alternative hypothesis typically

contests the status quo and may suggest a corrective action if true.

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.

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

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

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

H0: μD ≤ 5 H0: μD ≠ -2 H0: μD = 0

Which one of the following is not a scenario that exists when constructing a confidence interval for the difference in population means?

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

Which of the following is true about matched-pairs problems? Select all that apply.

Matched-pairs problems are similar to single sample problems because the individual differences are analyzed. There is no assumption requiring the population variances to be equal. Both sample sizes must be equal.

When H0: μ ≤ 150 and xx = 160, the p-value is defined as

P(xx ≥160).

In hypothesis testing, two incorrect decisions are possible:

Do not reject the null hypothesis when it is false. Reject the null hypothesis when it is true.

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

False

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.

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

Sum of squares / degrees of freedom

True or false: The test statistic for p is valid only if ¯P approximately follows a normal distribution.

True

The conclusions of a hypothesis test that are drawn from the p-value approach versus the critical value approach are

always the same.

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

analysis of variance

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 critical value approach specifies a region of values, called the ______. If the test statistic falls into this region, we reject the ______.

rejection region, null hypothesis

When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a

right-tailed test.

If the population standard deviation is unknown, it can be estimated by using ______.

s

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.

When the two estimates of variability are close to each other, this indicates

there is not enough evidence to reject the null. this variability could be due to chance.

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 between sample means variability within each sample.

Which of the following is true?

α = the probability of committing a Type I error; β = the probability of committing a Type II error.

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

The population correlation coefficients indicate a strong linear relationship.

The hypotheses H0: μ1 - μ2 ≥ d0 versus HA: μ1 - μ2 < d0 indicate a

left-tailed test.

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

μD

When testing μ, the probability of obtaining a sample mean at least as extreme as the one derived from a given sample, assuming that the null hypothesis is true, is called the

p-value

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

H0: μD ≥ d0; HA: μD < d0.

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

In hypothesis testing, if the sample data provide significant evidence that the null hypothesis is incorrect, then we

reject the null hypothesis.

When performing a hypothesis test on μ when the value of σ is unknown, the test statistic is computed as x−μ0/s÷√n and it follows the

tdf distribution with (n - 1) degrees of freedom.

When performing a hypothesis test on μ when the value of σ is unknown, the test statistic is computed as x−μ0s/√nx-μ0s/n and it follows the

tdf distribution with (n - 1) degrees of freedom.

We use hypothesis testing to

resolve conflicts between two competing hypotheses regarding a population parameter.

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

right tail of the distribution is α.

In comparing c population means, the ANOVA test assumes

the population variances are equal.

Which of the the following signs in the null would indicate a two-tailed test?

=

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

F decreases

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

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 .

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.

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.

The alternative hypothesis HA in one-way ANOVA is

Not all population means are equal.

If the collected sample data is inconsistent with what is stated in the null hypothesis, which decision is made?

The null is rejected and the alternative is accepted.

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

The z-distribution.

If the value of the test statistic falls in the rejection region, then the p-value must be

less than α.

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

means

When the population variances are unknown and not assumed equal, what are the degrees of freedom?

n1 + n2 - 2

The degrees of freedom for the within-treatments variance is

nT - c

A binomial distribution can be approximated by a ______ distribution for large sample sizes.

normal

Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are ______.

qualitative

For a hypothesis test of μ when σ is known, the value of the test statistic is calculated as

z = x−μ0 ÷ σ/√n

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a right-tailed test is (are):

z0.10

Which of the the following signs in the null would indicate a left-tailed test?

≥

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a left-tailed test is (are):

-z0.10

Suppose a hypothesis test is conducted at the α=0.05 level, the null would be rejected for p-values between

0 and 0.05

In ANOVA testing, if the ratio of the between-treatment variability to within-treatment variability is significantly greater than one, then we

reject the null hypothesis and conclude that not all population means are equal.

The hypotheses H0: μ1 - μ2 = d0 versus HA: μ1 - μ2 ≠ d0 indicate a

two-tailed test.

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

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

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.

For a hypothesis test on μ when the value of σ is unknown, the value of the test statistic is calculated as ______, provided that we sample from a normal population.

tdf = x−μ0 ÷ s/n√

The basic principle of hypothesis testing is to assume that

the null hypothesis is true and see if the sample data contradict this assumption.

A 100(1-α)% confidence interval can be used to test which types of hypotheses tests?

A two-tailed test at the α significance level.

Which of the following statements is NOT correct concerning the p-value and critical value approaches to hypothesis testing?

Both approaches use the same decision rule concerning when to reject H0.

Which one of the following is NOT a step we use when formulating the null and alternative hypotheses?

Calculate the value of the sample statistic.

When comparing two population means, their hypothesized difference

may assume any value.

An alternative hypothesis

contradicts the status quo

A test of H0: μ = 10 at the α significance level can be rejected if a 100(1-α)% confidence interval for μ

does not include 10.

Order the steps of formulating the competing hypotheses:

1. Identify the relevant population parameter of interest 2. Determine whether it is a one or two tailed test 3. Include some form of equality sign in the null hypothesis and use the alternative hypothesis

The null hypothesis is specified by using the following signs:

=, ≤, or ≥

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.

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

False

A Type II error occurs when we

Do not reject the null hypothesis when it is actually false.

In hypothesis testing, two incorrect decisions are possible:

Do not reject the null hypothesis when it is false. Reject the null hypothesis when it is true.

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

F

Which of the following are true about the F distribution? Select all that apply.

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.

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

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

The degrees of freedom for the between-treatments variance is

c - 1

We use ANOVA to determine ______.

if differences exist between the means of three or more populations

We can generally reduce both Type I and Type II errors simultaneously by

increasing the sample size.

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.

When examining the difference between two population means, if the populations cannot be assumed normal, then (XX1 - XX2) 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 (XX1 - XX2) follows a(n) ______ distribution.

normal

The hypothesis denoted by H0 is the ______ hypothesis and the hypothesis denoted by HA is the ______ hypothesis.

null, alternative

When H0: μ =12 and xx = 10, the p-value is defined as

p-value = 2 × P(Z ≤ z)

The alternative hypothesis is specified by using the following signs:

≠, <, or >