Chapter 18 Inferential Statistics Assignment 13

Inferential statistics are based on laws of probability.

Answer to Question #1

True

Inferential statistics, which are based on laws of probability, allow researchers to make inferences about a population based on data from a sample; they offer a framework for deciding whether the sampling error that results from sampling fluctuations is too high to provide reliable population estimates.

Inferential Statistics

A means of drawing conclusions about a population, given data from a sample

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Based on laws of probability

Sampling Distribution of the Mean

A theoretical distribution of means for an infinite number of samples drawn from the same population

Is always normally distributed

Has a mean that equals the population mean

Has a standard deviation (SD) called the standard error of the mean (SEM)

SEM is estimated from a sample SD and the sample size

Sampling Distribution

Question #2

Tell whether the following statement is true or false:

Point estimation through statistical procedures enables researchers to make objective decisions about the validity of their hypotheses.

Answer to Question #2

False

Hypothesis testing through statistical procedures enables researchers to make objective decisions about the validity of their hypotheses. Point estimation provides a single descriptive value of the population estimate.

Estimation of Parameters

Statistical inference—Two forms

Estimation of parameters

Hypothesis testing (more common)

Confidence Intervals

Used to estimate a single parameter

Two forms of estimation

Point estimation

Calculating a single statistic to estimate the population

Interval estimation

Calculating a range of values within which the parameter has a specified probability of lying

A confidence interval (CI) is constructed around the point estimate.

The upper and lower limits are confidence limits.

Hypothesis Testing #1

Based on rules of negative inference: Research hypotheses are supported if null hypotheses can be rejected.

Involves statistical decision-making to either

Accept the null hypothesis, or

Reject the null hypothesis

Hypothesis Testing #2

Researchers compute a test statistic with their data and then determine whether the statistic falls beyond the critical region in the relevant theoretical distribution.

If the value of the test statistic indicates that the null hypothesis is “improbable,” the result is statistically significant.

A nonsignificant result means that any observed difference or relationship could have resulted from chance fluctuations.