stats test 3

The ultimate goal in conducting a statistical test is ______.

to decide whether to retain the null hypothesis or to reject the null hypothesis

Which of the following is an important distinction between the z and t distributions?

the t distribution changes shape depending on sample size; the z distribution does not

The mean of the sampling distribution is equal to ______.

the true population mean

What is a critical value?

the value of z or t associated with a given A level

What prevents a researcher from positing direct inferences from a sample to a population?

the variation in sample statistics such as means and proportions

T/F: A range of values spanning a point estimate that is calculated so as to have a certain probability of containing the population parameter is the confidence interval.

true

T/F: A sample statistic such as a mean or proportion is also referred to as a point estimate in the field of statistics.

true

T/F: A sampling distribution is a theoretical distribution made up of infinite sample statistics.

true

T/F: Confidence levels are commonly set at .95 or .99 when working with large samples.

true

T/F: Expected outcomes are the results you anticipate seeing on the basis of probability theory.

true

T/F: Generally speaking, a sample needs to contain at least N ≥ 100 cases in order for the central limit theorem to be true.

true

T/F: In hypothesis testing, researchers make use of a probability distribution to find out whether a sample statistic has a low or high probability of occurrence.

true

T/F: In hypothesis testing, the key distinction is that between categorical and continuous variables.

true

T/F: In inferential statistics, the symbol used to denote an alternative hypothesis is H1.

true

T/F: In the construction of confidence intervals, the choice of the level of confidence is up to the discretion of the researcher.

true

T/F: In the t distribution, as sample size increases, the curve becomes more and more normal until it looks identical to the z curve.

true

T/F: The alternative hypothesis is essentially the opposite of the null hypothesis.

true

T/F: The c2 statistical test is an operation designed to be used with categorical data.

true

T/F: The probability of empirical outcomes is the basis of inferential statistics.

true

T/F: The t distribution is a unimodal distribution.

true

T/F: The t distribution resembles the z distribution in that it is symmetrical.

true

T/F: The α level itself is never used in the formula for the confidence interval. It is simply used to help determine the critical value.

true

T/F: Zα represents the probability that the confidence interval does not contain the actual population parameter.

true

Two-tailed tests have ______.

two critical values; one positive and one negative

A statistical test in which α is split in half and placed into both tails of the z or t distribution is called a ______.

two-tailed test

A ____ error occurs when a true null hypothesis is erroneously rejected.

type 1

A ______ error occurs when a true null hypothesis is erroneously rejected.

type 1

Approving an ineffective drug for the market is what kind of error?

type 1 error

If a researcher rejects the Ho when it is in fact true, what type of error has been made?

type 1 error

A ______ occurs when a false null is inaccurately retained

type 2 error

Incorrectly acquitting a guilty defendant is what kind of error?

type 2 error

The Greek symbol "σ" is used to represent which of the following?

the standard deviation for a population

The standard deviation of the sampling distribution is also called ______.

the standard error

There must be at least ______ successes and ______ failures in the sample in order to construct a confidence interval on the basis of proportions.

5;5

What is the area under the t distribution curve?

1.00

Generally is not advisable to work with samples smaller than ______.

100

A researcher has decided upon an α level of α = .05. Based on this, what is the chance that the confidence level the researcher calculates will not include the true population parameter?

5%

Confidence levels are set ______.

A priori; prior to the construction of the confidence interval

The hypothesis-testing procedure used when an independent variable is categorical with three or more classes and a dependent variable is continuous is ______.

ANOVA

Which kind of analytical test is used when the dependent variable is continuous and the independent variable is categorical with three or more classes?

ANOVA

A professor studying crime and environmental design has a sample of 25 neighborhoods. Which probability distribution should he use?

the t distribution

Which distribution is used to construct confidence intervals for means when N ≤ 99?

the t distribution

T/F: The probability that a confidence interval does not contain the true population parameter is represented by the Greek symbol x.

false

The level of confidence is defined as ______.

The probability that a confidence interval contains the population parameter

If a researcher had N = 120, which distribution would be used to construct a confidence interval?

Z

What acts as a sort of "bubble" that introduces flexibility into the estimate of the population parameter?

a confidence interval

What is meant by the term parameter?

a parameter is a number based on population data

An empirical distribution consisting of raw scores taken from a sample is referred to as ______ in scientific research?

a sample distribution

A theoretical distribution made up of infinite sample statistics is referred to as ______.

a sampling distribution

A two-tailed test is ______.

a statistical test in which A is split in half and placed into both tails of the z or t distribution

Confidence intervals are two-tailed because ______.

the normal curve has two halves that are divided by the mean

One of the most important theoretical ideas in statistics is the ______, which states that the sampling distribution will be normally distributed when infinite samples of a large size are drawn.

central limit theorem

A range of values that span a point estimate that is calculated so as to have a certain probability of containing the population parameter is called a ______.

confidence interval

______ are a way for researchers to use sample statistics to form conclusions about the probable values of population parameters.

confidence intervals

In the calculations for a confidence level involving a small sample, the acronym "df" stands for ______.

degrees of freedom

The term df' symbolizes what in the determination of a confidence interval with a small sample?

degrees of freedom

When trying to determine the critical value for t, it is first necessary to calculate the ______.

degrees of freedom

"Men are more likely to have a greater number of arrests than women" is what kind of hypothesis?

directional hypothesis

T/F: A population distribution contains a select subset of the values occurring within an entire population.

false

T/F: A sample distribution shows the shape and form of the values in a sample taken from a population.

false

T/F: Expected outcomes and observed outcomes are the results you anticipate seeing on the basis of probability theory.

false

T/F: In an inferential test, the statement predicting that there is no relationship between the independent and dependent variable is referred to as the alternative hypothesis.

false

T/F: In calculations for a confidence interval involving proportions, there is really no statistical difference between the population proportion, P, and the sample proportion,. It's simply a matter of two words designed to describe the same thing.

false

T/F: It can be assumed that a mean or standard deviation in a sample is an exact match to the mean or standard deviation in the population because often sample statistics are very similar, if not identical, to their corresponding population parameters.

false

T/F: It is relatively common for researchers to establish their level of confidence at 1.00, or 100%, as a time-saving tactic designed to increase reliability and validity.

false

T/F: Population parameters vary from sample to sample because of sampling error.

false

T/F: The area under the curve of the t distribution changes as sample size fluctuates. (T/F)

false

What is meant by the term inferential analysis?

it is the process of generalizing from a sample to a population; the use of a sample statistic to estimate a population parameter

_____ samples are more accurate representations of the population sample.

large

The proper test to use in any particular hypothesis-testing scenario is determined by the ______ of the variables you are using.

level of measurement

Zα represents what in statistics?

the probability that the confidence interval does not contain the true population parameter

If the Ho is true and a researcher retains it, which of the following scenarios has occurred?

the researcher has committed no error

The symbol ______ is used to denote a sample proportion in calculations for a confidence interval involving proportions

p

Which of the following is true with respect to researchers and the possibility of errors?

researchers can minimize the probability that they are wrong about a decision, but they can never eliminate it

In the t distribution, df is related to ______.

sample size

______ distributions are theoretical.

sampling

Which of the following is the reason that sampling distributions are theoretical constructs as opposed to empirical distributions?

sampling distributions are based on the notion of drawing infinite samples from a single population, something that is impossible in reality

Name a second characteristic of sampling distributions that make them different from empirical sample distributions.

sampling distributions are created not from raw scores but from sample statistics

Statistics vary from sample to sample because of ______.

sampling error

The fact that every sample that is drawn, and every sample that could potentially be drawn, has its own unique set of descriptive statistics, is called ______.

sampling error

The uncertainty introduced into a statistic by the fact that any sample that is drawn is one of infinite samples that could have been drawn and that a sample statistic is therefore not necessarily equal to the population parameters is the definition of ______.

sampling error

To account for ______ inferential statistics utilize sampling distributions to make probabilistic prediction about sample statistics

sampling error

Sample statistics vary from sample to sample. Why is this potentially problematic?

sampling error is introduced

When samples are ______, though the sampling distribution cannot be assumed to be normal.

small

In instances where N ≤ 99, researchers work with the ______ rather than the z distribution.

t distribution

In scientific research, the default assumption regarding the null and alternative hypotheses is ______.

that there is no relationship between the independent and dependent variables

The Greek symbol "μ" is used to represent which of the following?

the mean for a population