Ch. 9

Power is represented by

1-β

Given that β = .23 for a particular set of hypotheses, power =

1 - .23 = .77

When testing a population proportion, if either nπ0 or n(1-π0) are less than 10, one must calculate a p-value using the _________ distribution.

binomial

Hypothesis testing is used to test _________ and _________ in business and science.

Assumptions and theories

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

two-tailed and α stays the same.

True or false: Smaller values of α make it easier to reject the null.

False - harder

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

α/2

A business wants to use sample data to confirm that their average processing times have decreased after installing updated equipment. Their alternative hypothesis would be

H1: μ < μ0

A right-tailed hypothesis test for a mean resulted in tcalc = 2.23 with df = 16. If α = .05 the correct conclusion would be

Reject the null because the p-value < .05.

Which variables below would express proportion data?

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

The p-value method for testing hypotheses is often preferred by statisticians because

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

The test statistic used for testing μ when the population mean, σ, is unknown is

tcalc =x−μ0s/√n

A test statistic is

a standardized score of a sample statistic.

The significance level is the probability of making a

Type I error (α)

A quality control engineer would like to test if the average time of use for AAA batteries is equal to 8.5 hours. She does not know the population standard deviation. If a sample of 32 batteries is tested, the test statistic would be calculated as

tcalc=(x− - 8.5)/(s/sq root(32)), with df = 31

The difference between the sample statistic and the null hypothesis value is measured by a

test statistic.

The values of the chi square distribution range from zero to

Infinity

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

smaller

Given the following set of hypotheses: H0: Defendant is not guilty H1: Defendant is guilty, which statement describes the consequence of a Type II error?

The defendant is not convicted of the crime but was guilty.

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

critical

When calculating power for a proportion test, the power increases as the sample size increases and the more π ________________ from π0.

differs

The greater the difference between the true value of the population parameter and the null hypothesis benchmark value the __________ the value of power

greater

For a given sample size, reducing α results in an

increase in β.

All other things being equal, power will increase when the sample size

increases

The critical value stated in the decision rule is determined by

level of significance

The t statistic will approach the z score for a given value of α when

the sample size gets large (n > 30).

When calculating power for a proportion test one must know

the sample size n and significance level, α

A family of power curves for a two tailed test with μ0 = 12000 will have power values closer to ____________ when μ is close 12000 and closer to ____________ the further away μ is from 12000

0; 1

A service company would like to know if the proportion of customers satisfied with their service has changed since the last time they surveyed their customers. Their alternative hypothesis would be

H1: π ≠ π0

Alpha (α) is known as the significance ____________ and defines the rejection ____________

Level; region

When finding a p-value for a two-tailed test, it is important to _________ the tail area associated with zcalc by ________________ because the α area is split between the upper and lower tails

Multiply; 2

As the sample size, n, increases

P(Type II error) decreases and power increases

True or false: All business managers need a basic understanding of hypothesis testing.

True

True or false: If a confidence interval does not contain μ0, we can reject the null hypothesis in a two-tailed test for the same values of α.

True

An OC curve for a mean shows P(Type II error) on the ____________ axis and various values of the true ________________ on the horizontal axis.

Vertical; mean

If a 90% confidence interval for a store's customer accounts is computed as $850 ± 70, then the null hypothesis that μ = $750 would

be rejected at α = .10.

A statistical hypothesis test requires that we

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

It is possible to see a statistically 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.

The _____________ method is often preferred to the critical value method because it is a direct measure of the likelihood of observing the sample with the null hypothesis is true.

p-value

The definition of power is

rejecting the null hypothesis when the null is false.

When evaluating the variability of repair costs of a certain automobile, the population ___________ is an important component.

variance

When testing a hypothesis about a proportion and π0 = .3, then n ≥

34

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

False

True or false: Using a z score instead of t statistic to test a mean when sigma is unknown will increase Type II error.

False

A hypothesis is also known as an

assumption

A 95% confidence interval could be used to conduct a two-tailed hypothesis test when alpha is

.05

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

True or false: All statistically significant result have practical importance.

False

A hypothesis, or assumption, can be discarded or reformulated if the sample data is found to be ______________ with the hypothesis

inconsistent

We can generally reduce the probability of Type II errors by

increasing the sample size.

True or false: In the critical value approach, if a test statistic falls outside of the rejection region, then we can reject the null hypothesis.

False

True or false: If a critical value is set at 1.645 for a right-tailed test, a calculated test statistic of 1.82 would lead to the null hypothesis being rejected.

True - A value of 1.82 would be rejected because it is to the right of the critical value.

An example of the relevance of making inferences using a population variance is

a coffee vending machine wanting to put a certain amount of beverage in a cup, without being too little or spilling over.

The parameter value in the null hypothesis is called a ___________ and the value does not come from a _________________

Benchmark; sample

A manager tested the following hypotheses about the average days until an invoice was paid: H0: μ ≤ 15 vs.H1: μ > 15. The resulting p-value = .024. The level of significance used was .05. Which of the following is a valid conclusion?

The manager would reject the null hypothesis and conclude that the average number of days to pay an invoice was greater than 15.

All business managers need a basic understanding of hypothesis testing because

They often interact with specialists, they must make decisions based on statistical evidence and they are required to read and understand technical reports

Statistical inference regarding a population variance is based on the

chi-square distribution.

An OC curve stands for

operating characteristic (OC) curve

To find the left-tailed p-value for a test statistic tcalcusing Excel use the following formula:

=t.dist(tcalc, df, 1)

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.

Even though repeated hypothesis tests could result in no strong conflicts between the observed data and the null hypothesis, one would still not state the null has been proved, one would state that they would ____________ _____________ ___________the null hypothesis

Fail to reject

Given the following hypotheses: H0: π ≥ .25 vs. H1: π < .25, zcalc = -1.30 and the p-value is .0968. The level of significance is .10. Which is the appropriate conclusion?

Reject the null hypothesis and conclude that the population proportion is less than .25.

In hypothesis testing, there are 2 possible incorrect decisions:

Rejecting the null hypothesis when it is true and not rejecting the null hypothesis when it is false

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

True or false: A proportion can be expressed as percentage but not all percentages can be expressed as a proportion.

True

A power curve looks like an inverted

OC

____________ testing is used by business managers to guide decision making

Hypothesis

In hypothesis testing, 2 correct decisions are possible:

Rejecting the null hypothesis when the null hypothesis is false and not rejecting the null hypothesis when it is true.

Increasing the value of alpha in a hypothesis test will

make it less difficult to reject the null hypothesis,

In order to calculate the power a hypothesis test for a mean, the following information must be known:

significance level, α; a known or estimated value for σ; an alternative value for μ