data analysis and statistics chapter 9

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.

A Type II error occurs when we

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

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

at the expense of increasing β.

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.

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

increasing the sample size.

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

less than α.

We can reject the null hypothesis when the

p-value < α.

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

rejecting a true null hypothesis.

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

the sample test

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.

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 the equality sign as the null hypothesis and use the alternative hypothesis to establish a claim

When H0: μ ≥ 150 and xx = 125, the p-value is defined as

P(xx ≥125).

A Type I error occurs when we

Reject the null hypothesis when it is actually true.

The significance level is the allowed probability of making

a Type I error.

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

always the same.

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

no error.

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

The p-value is calculated assuming the

null hypothesis is true.

When performing a hypothesis test on μ when σ is known, H0 can be rejected for which of the following case?

p-value < α

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

qualitative

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

We use hypothesis testing to

resolve conflicts between two competing hypotheses regarding a population parameter.

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.

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−μ0s/√nx-μ0s/n and it follows the

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

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.

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

true

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

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