busi 2305 chap 9 smartbook

True or false: A Type I error occurs if we do NOT reject the null hypothesis when it is actually false.

False

Suppose the competing hypotheses for a test are H0: μ = 10 versus HA: μ ≠ 10. If the value of the test statistic is 1.87 and the critical values at the 5% level of significance are -z0.025 = -1.96 and z0.025 = 1.96, then the correct conclusion is:

Do not reject H0 and conclude that the population mean does not appear to differ from 10 at the 5% significance level.

In hypothesis testing, two correct decisions are possible:

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

The two equivalent methods to solve a hypothesis test are the

critical value approach. p-value approach.

A hypothesis test can be -tailed or -tailed

one two

If we reject the null hypothesis when it is actually false we have committed...

no error.

For an alternative hypothesis of HA: μ > μ0, we might possibly reject the null hypothesis if

the population mean is greater than μ0.

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 never be rejected if

z ≥ 0 for a left-tailed test.

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 5% significance level, the critical value(s) for a right-tailed test is (are):

z0.05

Consider the following competing hypotheses: H0: μ = 10 versus HA: μ ≠ 10. If a 95% confidence interval is [15, 20], then at the 5% significance level we

reject the null hypothesis and conclude that the population mean appears to differ from 10.

An auditor for a small business wants to determine whether the mean value of all accounts receivable is less than $550. She takes a sample of 40 and computes the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are

H0: μ ≥ 550 and HA: μ < 550

An auditor for a small business wants to test the assumption that the mean value of all accounts receivable differs from $550. She takes a sample of 40 accounts and calculates the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are

H0: μ = $550 and HA: μ ≠ $550

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 5% significance level, the critical value(s) for a two-tailed test is (are):

-z0.025 and z0.025

If the underlying population is not normally distributed, we need the sample size to be at least

30 or thirty

The p-value approach to hypothesis testing has steps.

4 or four

The null hypothesis is specified by using one of the following signs:

=, ≤, or ≥

Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus HA: μ > 10. If the value of the test statistic is 1.90 and the critical value at the 1% level of significance is z0.01 = 2.33, then the correct conclusion is:

Do not reject H0 and conclude that the population mean does not appear to be greater than 10 at the 1% significance level.

True or false: In the critical value approach, if the value of the test statistic does not fall within the rejection region, then we reject the null hypothesis.

False

Which of the following is NOT a step in the p-value approach to hypothesis testing?

Graph the distribution of the sample data

Which of the following are correctly configured one-tailed tests?

H0: p > p0 HA: p < p0 H0: μ < μ0 HA: μ > μ0 H0: p < p0 HA: p > p0 H0: μ > μ0 HA: μ < μ0

H0 HA

Null hypothesis Alternative hypothesis

True or false: Consider the following competing hypotheses: H0: μ = 150 versus HA: μ ≠ 150. If a 95% confidence interval is [100, 200], then we cannot reject the null hypothesis at the 5% significance level.

True

True or false: The optimal values of Type I and Type II errors require a compromise in balancing the costs of each type of error.

True

Rejecting the null hypothesis when the null hypothesis is true.

Type I error

We define α as the the probability of making a Type I error.

allowed or allowable

α is the probability of a Type I error.

allowed or allowable

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

always the same.

Hypothesis testing is analogous to a criminal court of law where someone is until proven

innocent guilty

It is not sufficient to end the analysis with a conclusion that you reject the null hypothesis or you do not reject the null hypothesis. You must the results.

interpret, report, or communicate

Not rejecting a true null hypothesis.

Correct decision

Specify the competing hypotheses that would be used in order to determine whether the population proportion is greater than 0.35.

H0: p ≤ 0.35 and HA: p > 0.35

Typically, the decision regarding the optimal level of Type I and Type II errors is made by the

management

The p-value is calculated assuming the

null hypothesis is true.

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.

Rejecting a false null hypothesis.

Correct decision

The alternative hypothesis for a one-sided test looks like:

HA: μ < μ0

The basic principle of hypothesis testing is to first assume that the ______ hypothesis is true and then determine if the sample data _______ this assumption.

null, contradict

The p-value is referred to as the probability of making a Type I error.

observed

When performing a hypothesis test on μ, the p-value is defined as the

observed probability of making a Type I error.

A one-tailed test involves a null hypothesis that can only be rejected on side of the hypothesized value.

one

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.

In inferential statistics, we use information to make inferences about an unknown parameter

sample population

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 left-tailed test is (are):

-z0.10

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.

Suppose the competing hypotheses for a test are H0: μ ≥ 10 versus HA: μ < 10. If the value of the test statistic is -2.50 and the critical value at the 5% level of significance is -z0.05 = -1.645, then the correct conclusion is:

Reject H0 and conclude that the population mean appears to be less than 10 at the 5% significance level.

Which of the following types of hypothesis tests may be performed?

Right-tailed, left-tailed, and two-tailed tests

The significance level is the probability of making

a Type I error.

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

at the expense of increasing β.

An important final conclusion to a statistical test is to...

clearly interpret the results in terms of the initial claim

We reject H0 if the p-value is alpha

less than

Which of the following is true?

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

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

increasing the sample size.

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.

Which of the following are correctly configured two-tailed tests?

H0: μ = μ0 HA: μ ≠ μ0 H0: p = p0 HA: p ≠ p0

In general, we follow three steps when formulating the competing hypotheses. Place these steps in the correct sequence

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

In order to implement an hypothesis test, it is essential that XX is distributed

normally

Hypothesis testing enables us to determine if the collected ______ data is inconsistent with what is stated in the null hypothesis.

sample

The only way we can reduce both Type I and Type II errors is by increasing

sample size

Put the following steps in the p-value approach to hypothesis testing in the correct order

specify the null and alternative hypotheses specify the significance level calculate the value of the test statistics and its p-value state the conclusion and interpret results

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

s

We always use evidence and the chosen significance level α to conduct hypothesis tests.

sample

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−μ0s/√nx-μ0s/n

By reducing the likelihood of a Type I error, we the likelihood of a Type II error,

increase or raise

The test statistic when the population standard deviation is know is z = x−μ0σ/√nx-μ0σ/n. This formula is valid only if XX follows a distribution

normal

The approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand.

critical value

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

less than α.

The alternative hypothesis typically _____

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

The optimal choice of α and β depends on the relative of these two types of errors.

cost

There are two equivalent methods to test a hypothesis: the p-value approach and the approach.

critical value

The p-value is the likelihood of obtaining a sample mean that is at least as as the one derived from the given sample, under the assumption that the null hypothesis is true as an equality.

extreme

A Type I error occurs when we the null hypothesis when it is true

reject

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

rejecting a true null hypothesis.