ISDS 2000 Exam 3 Review

It is not correct to conclude that

"we accept the null hypothesis"

The decision rule is

- Reject Ho if the p-value < a or - Do not reject H0 if p-value ≥ a

What are the 3 steps when 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 in the null hypothesis and use the alternative hypothesis to establish a claim.

4 Step Procedure Using the p-Value Approach

1. Specify the null and alternative hypothesis. 2. Specify the significance level. 3. Calculate the value of the test statistic and the p-value. 4. State the conclusion and interpret results.

What are the two approaches to implementing a hypothesis test?

1. p-value 2. critical value approach

The significance level of a hypothesis is defined as ______?

100a%

The null hypothesis is specified with which one of the following signs

= , ≤ , ≥

If Ha: μ < μ0

Left-tailed probability: P(Z ≤ z)

If Ha: μ > μ0

Right-tail probability: P(Z ≥ z)

T/F For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.

True

If Ha: μ ≠ μ0

Two-tail probability: 2P(Z ≥ z) if z > 0 or 2P(Z ≤ z) if z<0

A(n) ___________ error is committed when we reject the null hypothesis when the null hypothesis is true.

Type I

As a general guideline, we use the ____________ ____________ as a vehicle to establish something new-that is, contest the status quo.

alternative hypothesis

Alternative Hypothesis (Ha)

contradicts the default state or status quo specified in the null hypothesis

Null Hypothesis (H0)

corresponds to a presumed default state of nature or status quo

Which approach is attractive when a computer is unavailable and all calculations must be done by hand?

critical value approach

If sample evidence is NOT inconsistent with the null hypothesis, we

do NOT reject the null hypothesis

Degrees of Freedom (df) =

n - 1

The p-value is also referred to as the __________ _________ of a Type I error.

observed probability

A hypothesis test can be ________ or __________.

one-tailed or two-tailed

The parameter p represents the

proportion of observation with a particular attribute

If sample evidence is inconsistent with the null hypothesis, we...

reject the null hypothesis

We use the hypothesis testing framework to

resolve conflicts between two competing hypotheses on a particular population parameter of interest

Test Statistic for μ when σ is unknown

tdf = x̄- μ0 s /√n

Significance level

the allowed probability of making a Type I error

The null hypothesis in a hypothesis test refers to ...?

the default state of nature

p-value

the likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample

If the chosen significance level is a = 0.05 then, ...?

there is a 5% probability of rejecting a true null hypothesis

Type II Error

this error occurs when the decision is to not reject the null hypothesis when the null hypothesis is false

Type I Error

this error occurs when the decision is to reject the null hypothesis when the null hypothesis is true

Two-tailed test

we can reject the null hypothesis on either side of the hypothesized population parameter. Ex: H0: μ = μ0 vs Ha: μ ≠ μ0

One-tailed test

we can reject the null hypothesis only on one side of the hypothesized value of the population parameter. Ex: H0: μ ≥ μ0 vs Ha: μ < μ0

We conduct a hypothesis test to determine

whether or not sample evidence contradicts the null hypothesis

Test Statistic for μ when σ is known

z = x̄- μ0 / σ /√n

Test Statistic for p

z= (p-po) / √(po(1-po)/n)

The alternative hypothesis is specified with which of the corresponding opposite signs

≠ , <, >