Chapter 9 LearnSmart (Norwood)

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 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.

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.

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

False

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

Graph the distribution of the sample data.

A researcher for a store chain wants to determine whether the proportion of customers who try out the samples being offered is more than 0.15. The null and alternative hypotheses for this test are

H0: p ≤ 0.15 and HA: p > 0.15

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.

The test statistic when the population standard deviation is know is z = x−μ0σ/√nx-μ0σ/n. Match each term to its meaning. Z X (x-bar) μ0 σ n

The test statistic The sample mean The hypothesized mean The population standard deviation The sample size

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

allowable

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

The formula z = p−p0√p0(1−p0)np-p0p0(1-p0)n is valid only if PP follows a _______ distribution.

normal

When testing μ, the p-value is the probability of obtaining a sample mean at least as extreme as the one derived from a given sample, assuming that the______ hypothesis is true.

null

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

observed

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

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

As a point estimate of the population proportion, we calculate ______.

p-bar

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)

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

z = p−p0√p(1−p)n

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

A Type I error is commonly denoted as:

α (alpha)

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

S

α is the _______probability of a Type I error.

allowable

True or false: Given a right-tailed hypothesis test, if the value of the test statistic is 1.82 and the critical value is 1.645, then we do not reject the null hypothesis.

False

A Type I error occurs when we...

reject the null hypothesis when it is actually true.

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.

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

reject

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.

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

sample