STAT Chapter 10

Hypothesis Testing

1) Hypotheses: H0 = x and H1(<, >, or /=) x Let (p or u) = the true (proportion or mean) 2) Conditions: -Data collection used SRS -n < .05N -np(1-p) >= 10 (proportion) or population is normally distributed/ n>30 (mean) 3) Test Statistic: either: z or t 4) P-Value look up in Z or T chart can be x < p-value < x Two-tailed test: multiply by 2 5) Conclusion -If P-value is < alpha, reject H0, and there is sufficient evidence to support the claim in H1 (statistically significant) -If P-value is > alpha, do not reject H0, and there is not sufficient evidence to support the claim in H1

Hypothesis

A statement about the nature of the population, usually regarding the value of a population parameter such as p or u

Test Statistic

A statistic computed from sample data that the researchers use to decide between the null and alternative hypotheses. -quantifies the difference between the point estimate for the parameter and its null hypothesis value, usually by the number of standard errors between them

Null Hypothesis

Denoted H0, the claim to be tested. It states that the population parameter is equal to a particular value, and is assumed to be true unless sufficient evidence is gathered to reject it.

Alternative Hypothesis

Denoted H1 or Ha, is the research hypothesis. It is the statement that one wishes to find evidence to support as being true. It states that the population parameter falls in some alternative range of values

Left-Tailed Test

H0: parameter = some value H1: parameter < some value

Right-Tailed Test

H0: parameter = some value H1: parameter > some value

Two-Tailed Test

H0: parameter = some value H1: parameter not equal to some value

Decision 1

If the sample data are consistent with the null hypothesis, we DO NOT REJECT H0, and state that there is not sufficient evidence to support the alternative hypothesis

Decision 2

If the sample data are inconsistent with the null hypothesis and supportive of the alternative, we REJECT H0, and state there is sufficient evidence to support the alternative hypothesis.

Type II Error

Occurs if we do not reject the null hypothesis when the alternative hypothesis is true (Failure to Reject, B)

Type I Error

Occurs if we reject the null hypothesis when the null hypothesis is true (Reject, a)

P-Value

Represents the probability that the test statistic takes the observed value or a value more extreme in the direction of the alternative hypothesis if the null hypothesis is true. -Small P-values represent strong evidence against the null hypothesis

Level of Significance

The probability of making a Type I error, a. -0.01, .05, .10 -Reducing a will increase B (they are inversely related)