[STATS FINAL] T&D

discrete, continuous

Random variables can be either ___ or ___.

continuous random variables

___ can assume all values between any two given values of the variables.

approximately normally distributed variables

Continuous variables whose distributions are bell-shaped are called ___.

mean, standard deviation

The shape and position of the normal distribution curve depend on two parameters, the ___ and the ___.

standard deviation

The larger the ___, the more dispersed or spread out the normal distribution becomes.

population mean

μ stands for the ___.

population standard deviation

σ stands for the ___.

bell-shaped, symmetrical

The normal distribution curve is ___ and ___ about the mean.

unimodal, continuous

A normal distribution curve with a single mode is ___, and a curve with no gaps is ___.

mean, median

The ___ and ___ are equal to the mode and located at the center of the normal distribution.

x-axis

The normal distribution curve never touches the ___.

1 or 100%

The total area under the normal distribution curve is equal to ___.

standard normal distribution

A normal distribution with a mean of 0 and a standard deviation of 1 is called the ___.

standard score

The value used to transform any normally distributed variable into the standard normally distributed variable is the ___.

standard deviations

A z value is the number of ___ that the x value is from the mean.

z table

A table of areas under the standard normal curve is called the ___.

0 and a specified z

The z table gives the area under the standard normal curve between ___.

positive

Although z values can be negative, areas must be ___.

0.5

The area under the standard normal curve to the right of z = 0 is ___.

symmetry

The area between negative z and 0 equals the area between 0 and z because of ___.

tail area

An area to the right of a positive z value, or to the left of a negative z value, is called a ___.

standardizing a normal distribution

Converting a normal distribution to the standard normal distribution is called ___.

probability

The area under the normal distribution curve corresponds to a ___.

P(0 < z < 1.5)

The probability of any z value between 0 and 1.5 is written as ___.

right tail, left tail

P(z > a) is a ___ area, while P(z < a) is a ___ area.

hypothesis testing

___ is a decision-making process for evaluating claims about a population.

z test, t test

The two specific statistical tests for hypothesis testing on means are the ___ and the ___.

chi-square test

The ___ is used for testing the standard deviation.

statistical hypothesis

A ___ is an inference about a population parameter.

entire population

The only sure way of finding the truth or falsity of a hypothesis is by examining the ___.

sample

Because examining the entire population is not always feasible, a ___ is examined instead.

population, hypotheses

The researcher must define the ___ under study and state the particular ___ to be investigated.

significance level, sample

The researcher must give the ___ and select a ___ from the population.

data, required test

The researcher must collect the ___ and perform the ___, then reach a conclusion.

claim, mathematical symbols

To state the hypotheses correctly, the researcher must translate the ___ into ___.

null hypothesis

The ___, symbolized as Ho, states that there is no difference between a parameter and a specific value.

alternative hypothesis

The ___, symbolized as Ha, states a specific difference between a parameter and a specific value.

two-tailed test

Ho: parameter = specific value versus Ha: parameter ≠ specific value is a ___.

left-tailed test

Ho: parameter = specific value versus Ha: parameter < specific value is a ___.

right-tailed test

Ho: parameter = specific value versus Ha: parameter > specific value is a ___.

one-tailed test

A ___ indicates that the null hypothesis should be rejected when the test value is in the critical region on one side of the parameter.

right-tailed, left-tailed

A one-tailed test is ___ when the alternative hypothesis uses greater than (>), and ___ when it uses less than (<).

Type I error

A ___ occurs if one rejects the null hypothesis when it is true.

Type II error

A ___ occurs if one does not reject the null hypothesis when it is false.

level of significance

The ___ is the maximum probability of committing a Type I error.

alpha, beta

The probability of a Type I error is symbolized by ___, and the probability of a Type II error is symbolized by ___.

beta

In most hypothesis testing situations, ___ cannot be computed.

0.10, 0.05, and 0.01

Statisticians generally agree on three arbitrary significance levels: ___.

10%, 5%, or 1%

If the null hypothesis is rejected, the probability of a Type I error is ___ at the 0.10, 0.05, and 0.01 levels respectively.

90%, 95%, or 99%

If the null hypothesis is rejected, the probability of a correct decision is ___ at the 0.10, 0.05, and 0.01 levels respectively.

5%

When α = 0.05, there is a ___ chance of rejecting a true null hypothesis.

seriousness of the Type I error

The level of significance the researcher uses depends on the ___.

critical value

After a significance level is chosen, a ___ is selected from a table for the appropriate test, and it determines the critical and noncritical regions.

critical region

The ___, or rejection region, is the range of values of the test value that indicates a significant difference and that the null hypothesis should be rejected.

noncritical region

The ___, or non-rejection region, is the range of values of the test value that indicates the difference was probably due to chance.

reject, do not reject

If the test value falls in the critical region, ___ the null hypothesis; if it falls in the noncritical region, ___ the null hypothesis.

positive, negative

A two-tailed test has two critical values, one ___ and one ___.

negative, positive

The critical value of a left-tailed test is ___, while that of a right-tailed test is ___.

α/2

In a two-tailed test, the area in each tail is ___.

state the null and alternative hypotheses

The first step in hypothesis testing is to ___.

select the level of significance

The second step in hypothesis testing is to ___.

determine the critical value and the rejection region/s

The third step in hypothesis testing is to ___.

state the decision rule

The fourth step in hypothesis testing is to ___.

compute the test statistic

The fifth step in hypothesis testing is to ___.

make a decision, whether to reject or not to reject the null hypothesis

The sixth step in hypothesis testing is to ___.

observed value, expected value

A test value is the ___ minus the ___, divided by the standard error.

observed value

The ___ is the statistic, such as the mean, that is computed from the sample data.

expected value

The ___ is the parameter one would expect to obtain if the null hypothesis is true.

standard error

The denominator of a test value is the ___ of the parameter being tested.

z test

The ___ is a statistical test for the mean of a population that can be used when n≥30, or when the population is normally distributed and σ is known.

sample mean, hypothesized mean

In the z test, X̄ is the ___ and μ is the ___.

population standard deviation, sample size

In the z test, σ is the ___ and n is the ___.

t test

The ___ is a statistical test for the mean of a population that is used when the population is normally or approximately normally distributed, σ is unknown, and n<30.

sample standard deviation

In the t test, since the population standard deviation is unknown, the ___ is used.

degrees of freedom

In the t test, d.f. stands for ___ and equals n minus 1.

t table

The critical values for a t test are found in a ___.