ch 9 isds reading questions

Regardless of the distribution used, the numerator is

(XX1 - XX2) - d0

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 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

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 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

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

=

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 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.

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.

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.

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.

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

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

F decreases

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

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

False

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

Fdf1,df2 distribution.

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

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

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.

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

H0: μD ≥ d0; 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.

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.

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.

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.

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.

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.

The alternative hypothesis HA in one-way ANOVA is

Not all population means are equal.

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

P(xx ≥160).

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

Sum of squares / degrees of freedom

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.

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

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.

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

The population correlation coefficients indicate a strong linear relationship.

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.

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.

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

The z-distribution.

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

True

The significance level is the allowed probability of making

a Type I error.

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.

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 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.

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

The degrees of freedom for the between-treatments variance is

c - 1

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

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

df2 α df1

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.

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.

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

left-tailed test.

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

less than α.

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

margin of error.

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

matched-pairs sampling.

When comparing two population means, their hypothesized difference

may assume any value.

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

mean difference.

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

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.

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

The normal distribution approximation for a binomial distribution is valid when

np ≥ 5 and n(1 - p) ≥ 5

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

We can reject the null hypothesis when the

p-value < α.

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

p-value = 2 × P(Z ≤ z)

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

qualitative

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 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.

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.

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

reject the null hypothesis.

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

rejecting a true null hypothesis.

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

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

right tail of the distribution is α.

The one-way ANOVA test is always a

right tailed test

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

We would conduct a hypothesis test to determine whether or not

sample evidence contradicts H0.

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

tdf = d−d0sD/n√

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√

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.

The p-value is calculated assuming the

the null hypothesis is true

The basic principle of hypothesis testing is to assume that

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

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

the percentage of students living off-campus.

In comparing c population means, the ANOVA test assumes

the population variances are equal.

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

the sample test

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.

The critical value of a hypothesis test is

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

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.

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

two-tailed test.

We calculate a pooled estimate of the common variance by

using weighted averages of the sample variances.

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.

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 √

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

z = x−μ0 ÷ σ/√n

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.

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

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

zero

Which of the following is true?

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

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

μD

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

≥

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

≥ α.