Chapter 8

If the odds of getting the observed difference are less than 0.05, we will reject the null hypothesis

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Student's T Distribution

A distribution used to find the critical region for tests of sample means when s is unknown and the sample size is small As sample size increases, the t distribution resembles the Z distribution more and more until, with sample sizes greater than 120, the two distributions are essentially identical

One vs Two Tail Tests

A one-tailed test is more likely to reject Ho without changing the alpha level

Null Hypothesis

A statement of "no difference." In the context of single-sample tests of significance, the null hypothesis states that the population from which the sample was drawn has a certain characteristic or value.

Research Hypothesis

A statement that contradicts the null hypothesis. In the context of single-sample tests of significance, the research hypothesis says that the population from which the sample was drawn does not have a certain characteristic or value.

One-Tailed Test

A type of hypothesis test used when (1) the direction of the difference can be predicted OR (2) concern focuses on outcomes in only one tail of the sampling distribution Questions using terms: greater, more than, less than, etc.

Two-Tailed Test

A type of hypothesis test used when (1) the direction of the difference cannot be predicted OR (2) concern focuses on outcomes in both tails of the sampling distribution Questions that do not use directional terms

Type I and II Errors

As the alpha level decreases... -The probability of a Type I error decreases -The probability of a Type II error increases The two types of error are inversely related Higher alpha levels will minimize the probability of Type II errors Lower alpha levels will minimize the probability of Type I errors

Z or T distribution?

If population standard deviation (o) is... -Known, use Z distribution -Unknown and sample size (N) i large, use Z distribution -Unknown and sample size (N) is small, use t distribution

Hypothesis Testing/Significance Testing

Statistical tests that estimate the probability of sample outcomes if assumptions about the population (the null hypothesis) are true

Z(critical)

The Z score that makes the beginnings of the critical region on a Z distribution

Critical Region/Region of Rejection

The area under the sampling distribution that, in advance of the test itself, is defined as including unlikely sample outcomes, given that the null hypothesis is true. The shaded area is the critical region.

Type II Error (Beta Error)

The probability of failing to reject a null hypothesis that is, in fact, false

Type I Error (Alpha Error)

The probability of rejecting a null hypothesis that is, in fact, true

Alpha Level

The proportion of area under the sampling distribution that contains unlikely sample outcomes, given that the null hypothesis is true. Also, the probability of Type I error. The size of the critical region is reported as alpha, the proportion of all of the area included in the critical region.

Z(obtained)

The test statistic, sample outcomes expressed as a Z score

Test Statistic

The value that converts the sample outcome into either a t score or z score

t(critical)

the t score that makes the beginning of the critical region of a t distribution

t(obtained)

the test statistic, sample outcome expressed as a t score