Qa-233 Hypothesis Testing

Front 1

Rejecting Ho when it’s actually true:

Back 1

Type I error

Front 2

Ho can only be what 3 symbols?

Back 2

(≥, =, or ≤)

Front 3

The smallest significance level at which the null hypothesis will not be rejected:

Back 3

The p-value

Front 4

Scientific method-based means for using sample data to evaluate conjectures about a population:

Back 4

Hypothesis Testing

Front 5

What happens if p-value < α ?

Back 5

Then we reject the null hypothesis

Front 6

Sample statistic used to decide whether to reject or fail to reject the null hypothesis:

Back 6

Test statistic

Front 7

This is equivalent to a claim that the difference between the observations and the hypothesized value are due to random variation:

Back 7

Ho: the null hypothesis

Front 8

The probability of committing a type I error:

Back 8

The level of significance (denoted by α)

Front 9

Failing to reject Ho when it’s actually false:

Back 9

Type II error

Front 10

What type of probability distribution is the p-value?

Back 10

A conditional probability distribution

Front 11

The set of all values which would cause you to reject the null hypothesis, Ho:

Back 11

Critical region

Front 12

What happens if p-value > α?

Back 12

Then we do not reject the null hypothesis

Front 13

What is Ha?

Back 13

The alternative hypothesis
that tells us what type of test we are using. Can be (>, ≠, or <)

Front 14

A statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis":

Back 14

Decision Rule

Front 15

A test of whether the population mean is different from the hypothetical mean:

Back 15

2-tailed test

Front 16

This is equivalent to a claim that the difference between the observations and the hypothesized value are systematic (i.e., due to something other than random variation):

Back 16

Ha: the alternate hypothesis

Front 17

Why are p-values preferred?

Back 17

1) They allow anyone to select their own significance level a.
2) They provide a measure of the strength of the evidence the sample data provides against the null hypothesis (smaller p-value – stronger evidence against Ho).
3) They are usually reported by computer packages.

Front 18

When the null hypothesis is true, but the sample information has resulted in the rejection of the null, a ____ has been made.

Back 18

Type I Error

Front 19

What happens if the level of significance (a) is made smaller?

Back 19

The critical (rejection) region becomes larger.

Front 20

The maximum probability of a Type I error that the decision maker will tolerate:

Back 20

Level of significance

Front 21

What increases the chances of making a Type I Error?

Back 21

Increasing the signficance level (i.e. from .01 to .05)

Front 22

The values that mark the boundaries of the critical region:

Back 22

Critical values

Front 23

If the level of significance of a hypothesis test is increased from .01 to .05, the probability of a Type II error

Back 23

Will be decreased

Front 24

Claim that the difference between the observations and the hypothesized value are systematic and caused by something other than random variation:

Back 24

Ha - the alternate hypothesis

Front 25

Hypothesis test for which sample results that are only sufficiently less than the conjectured value of the parameter:

Back 25

Lower-tailed test

Front 26

The smaller the _____ the greater evidence against ____.

Back 26

P-value, Ho

Front 27

List the 6 steps in Hypothesis Testing:

Back 27

1) State the null and alternative hypotheses.
2) Select your test statistic.
3) State the level of significance a, and find the critical values/p-value.
4) Calculate the test statistic.
5) Decide whether to reject or not reject the null hypothesis.
6) Interpret your results.

Front 28

As z gets larger, ___ gets smaller.

Back 28

P-value

Front 29

What is the z-value for a two-tailed hypothesis test on a population mean when alpha is 5%?

Back 29

1.96

Front 30

The power of a statistical test is the probability of rejecting the null hypothesis when it is _______. When you increase alpha, the power of the test will _______.

Back 30

False, increase

Front 31

The quantity (1 - alpha) is called:

Back 31

The confidence coefficient

Front 32

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ____.

Back 32

Decrease

Front 33

In testing for differences between the means of two related populations the null hypothesis states that:

Back 33

The population mean difference is equal to 0

Front 34

When testing for a difference in two population means from small samples, a pooled variance must be computed when ___________.

Back 34

Variances are assumed to be equal

Front 35

The point that divides the non-reject region from the rejection region:

Back 35

Critical value

Front 36

When will we use the z test?

Back 36

1) The population is normally distributed.
2) The population standard deviation is known.
3) The population standard deviation is not known, but the sample size n>30 (in this case we will use Sx).

Front 37

As the number of ____ increase(s), the shape of the t distribution approaches the standard normal distribution.

Back 37

Degrees of freedom

Front 38

A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the degrees of freedom are

Back 38

n1 + n2 - 2 = 10 + 8 - 2 =16

Front 39

What assumptions are necessary for a two-sample hypothesis test about the difference between two LARGE SAMPLE means?

Back 39

1) The two populations must be independent (unrelated).
2) The samples must be large enough so that the distribution of the sample means follows the normal distribution (i.e. n1>30, n2>30).

Front 40

"Before" and "after" samples often characterized by a measurement:

Back 40

Dependent (matched) samples

Front 41

What assumptions are required when testing a hypothesis about the difference between two SAMPLE SAMPLE means?

Back 41

1) The sample populations follow the normal distribution.
2) The two samples are from independent populations.
3) The standard deviations of the two populations are EQUAL.

Front 42

Which selection on your TI-83 would be used to answer the question “How much more do Lamborghini owners spend per year on maintenance than Subaru owners?”

Back 42

2-SampTInterval

This is unpaired numeric data