Data Analysis: Chapter 9: One-Sample Hypothesis Tests

We can generally reduce the probability of Type II errors by ____.

increasing the sample size

The critical value is determined by the chosen ______ of _________.

level; significance

The mean of the sampling distribution of p is the _______ proportion.

population

p-value method

requires that you express the strength of your evidence against the null hypothesis in terms of probability. - a direct measure of the likelihood if the observed sample under H0.

The _______ the p-value, the more inclined we are to reject the null hypothesis.

smaller

decision rule

states what the critical value of the test static would have to be in order to reject H0 at the chosen level of significance (alpha)

The critical value of z for a left-tailed test with Alph = .05 is _____.

-1.645

A left-tailed hypothesis test for a mean resulted in tcalc=-1.50 with df=29. The p-value would be in what range?

.05 < p-value <.10

For a right-tailed test with zcalc=1.45, the p-value is ________. (round to four decimals)

.0735 use excel function =(NORM.S.DIST(1.45,1). Get your answer and subtract it from 1 to get the right tail

Alpha is known as the significance ______ and defines the rejection _____.

level; region

test statistic

measures the difference between a given sample mean and a benchmark in terms of rate standard error of the mean - is the standardized score of the sample statistic

A type II error is made when we fail to reject the ______ hypothesis when it is actually false.

null

The p-value is the probability of obtaining a sample mean as extreme as the one observed, assuming the ______ hypothesis is true.

null

type 1 error

reject a true hypothesis - represented by alpha - also called a false positive - P(reject H0 given H0 is true)

critical value

the boundary between the two regions (reject H0, do not reject H0).

Given the following set of hypotheses: H0: No illegal steroid use; H1: illegal steroid use; which statement describes the consequence of a Type I error?

An athlete is banned from competing when he or she did not use illegal steroids

For a two-tailed test with zcalc=0.78, the resulting p-value is _____. (round to 4 decimals)

.4354

The power of a test is measured by ___.

1-B

level of significance

referred to as alpha the probability of a Type 1 error (rejecting a true null hypothesis) is denoted by alpha.

The t-statistic assumes that the population is normally distributed. However, t-test results are considered fairly ________ to non-normality as long as there are no _____.

robust; outliers

rejection region

the area under the sampling distribution curve that defines an extreme outcome

For a two-tailed test of a proportion, zcalc=1.30. The p-value is _____.

.1936

It is possible to see a statically significant change in a population parameter even though the difference does not have practical implications _________.

if a very large sample was taken which can illuminate very small changes in a population mean.

power

correctly reject a false hypothesis - represented as 1-beta - also called sensitivity - P(reject H0 given H0 is false) - larger samples lead to increased power

A decision rule states what the value of the test statistics must be in order to reject the null hypothesis. This value is called the ____ value.

critical

type 2 error

fail to reject a false hypothesis - represented as beta - also called a false negative - P(fail to reject H0 given H0 is false)

True or false: A Type I error is when we FAIL to reject the null hypothesis when it is actually false.

false

True or false: smaller values of alpha make it easier to reject the null.

false; smaller values make it harder

True or false: A null hypothesis can be proved true.

false; we can only reject the null hypothesis

We would not reject the null hypothesis when the p-value is _______.

1. close to 1.0 2. greater than the level of significance

A statistical hypothesis test requires that we ____

1. determine whether it is a one or two tailed test 2. identify the population parameter of interest

Hypothesis testing as an ongoing process

1. get idea 2. formulate hypotheses 3. garter data 4. fint test statistic 5. make a decision 6. revise your ideas

The p value method for testing hypotheses is ofter preferred by statistics because ______

1. it expresses the strength of your evidence against the null 2. it is more flexible than the critical value method

In hypothesis testing, 2 correct decisions are possible:

1. not rejecting the null hypothesis when it is true 2. rejecting the null hypothesis when the null hypothesis is false

Order the steps used in hypothesis testing.

1. state they hypothesis 2. specify the decision rule 3. collect data 4. make decision 5. take action

Which variables below would express proportion data?

1. the number of customers who agree that the new product price is acceptable 2. the number of employees who reported an accident last month

All business managers need a basic understanding of hypothesis testing because______.

1. they often interact with specialists 2. they are required to read and understand technical reports 3. they must make decisions based on statistical evidence

A researcher for a store chain wants to test the assumption that the mean proportion of all people who stop in the store(s) who try the samples offered is 0.15. She thinks that the proportion is actually higher than 0.15. The null and alternative hypotheses for this test are ________.

H0: pie </ 0.15 and H1: pie > 0.15

A business believes their supplier's delivery times have been increased over the past few months. To test this belief they would use which alternative hypothesis?

H1: μ > μ0

Which of the following are NOT options in Excel for calculating a p-value from a t distribution?

T.Dist.Lt

A Type I error is commonly denoted by the symbol _____.

a (alpha)

hypothesis test

a decision between two competing, mutually exclusive, and collectively exhaustive hypotheses about the value of the parameter

A test statistic is ___.

a standardized score of a sample statistic

statistical hypothesis

a statement about the value of a population parameter that we are interested in

Using the critical value method for a two-tailed test, the critical value is determined by a tail area equal to _____

a/2 a= alpha

Which of the following is true?

a= the probability of committing a Type I error B= the probability of committing a Type II error

An alternative hypothesis is also called ____

an action alternative

A hypothesis is also known as an ____.

assumption or theory

The parameter value in the null hypothesis is called a ______ and the value does not come from a ______.

benchmark; sample

______ testing is used by business managers to guide decision making.

hypothesis

For an alternative hypothesis of H1: u> u0, we would reject the null hypothesis only when _______

the sample mean is greater then u0

The t statistic will approach the z score for a given value of alpha when ________.

the sample size gets large (n>30).

True or false: If a confidence interval does not contain u0, we can reject the null hypothesis in a two-tailed test for the same values of alpha.

true

A confident interval can be used to test a hypothesis if the hypothesis test is _________

two-tailed and alpha stays the same

We can reject the null hypothesis ______.

when the p-value < a

A sample proportion p is calculated by ____.

x/n