Chapter 8 - Testing Means: One-Sample T Test with Confidence Intervals

the T statistic

determines the number of standard deviations in a t distribution that a sample deviates from the mean value or difference stated in the null hypothesis

To compute a Z obt score...

population variance must be known *In behavioral science, it is rare that the variance in a population is known

Proportion of Variance

proportion or percent of variability in a dependent variable that can be explained or accounted for by a treatment

As sample size increases...

sample variance more closely resembles population variance

The estimated standard error in the t-statistic uses the ___ to estimate the ____ when the population variance is unknown.

sample variance, population variance

3 measures of effect size

1. estimate Cohen's D 2. Eta-squared (tends to overestimate) 3. Omega-squared (more conservative estimate)

A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test?

31 N - 1 = DF

It is most appropriate to report effect size with a significant result. Why is it generally inappropriate to report effect size with nonsignificant results?

Because it makes little sense to report the size of an effect that you just concluded does not exist

Estimated Cohen's d

number of standard deviations that mean scores shift above or below the population mean stated by the null hypothesis

As degrees of freedom for a t test increase, the critical values for that test also increase.

False

The critical values are reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

False

The t distribution is similar to the z distribution except

(all answers are correct), associated with scores being more likely in the tails of the distribution, associated with greater variability, and characterized by "thicker" tails compared with z distribution

3 Assumptions

1. Normality - normally distributed 2. Random Sampling 3. Independence - probabilities of each measured outcome in a study are independent

Alternative proposed by William Sealy Gosset

Estimated Standard Error - substitute the population variance with the sample variance in the formula for standard error. This is the denominator of the test statistic for a T test.

A researcher records the number of distracters that preschool-aged children ignored while watching a popular Sunday morning cartoon show. Assuming the population variance is unknown, what type of t test is appropriate for this study?

One-sample T test

Estimated Standard Error

an estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unknown variance

As a requirement for the t test, researchers compute any type of t test with samples selected from populations in which _____

the population variance is unknown

To compute a one-sample t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?

the population variance must be known

As N increases

the probability of outcomes in the tails become less likely and the tails approach the x-axis faster

A researcher states that the average child acquires 2.6 taste aversions in his or her lifetime. This is an example of a point estimate.

True

Sample variance is an unbiased estimator of the population variance.

True

T distribution

mathematically defined curve that is the comparison distribution used in a t test normally distributed but with greater variability in the *tails*