Unit 1.1

Hypotheses

to check whether the data support certain statements or predictions

Hypothesis

a statement about a population usually claiming that a population parameter takes a particular numerical value or falls in a certain range of values.

Significance test

is a method or using data to summarize the evidence about a hypothesis.

probability

provide a way to quantify how plausible a parameter is while controlling the chance of an incorrect inference

Steps in Significance Testing

Step 1: Assumptions

Step 2: State the hypotheses

Step 3: Compute for the Test Statistic

Step 4: Interpret the Test Statistic

Step 5: Make a conclusion

Assumptions

-Each significance test makes certain assumptions or has certain

conditions under which it applies.

-A test assumes that the data production used randomization.

-Assumptions may be about the sample size and/or about the shape of the population distribution.

State the hypothesis

is a statement about a population, usually claiming that a parameter takes a particular numerical value or falls in a certain range of values

categorical variable

parameter is a proportion, p

quantitative variable

the parameter is a mean, μ

Null hypothesis

-is a statement that the parameter takes a particular value

-Ho

(=,>=,<=)

Alternative Hypothesis

• ≠, >, <

test statistic

describes how far that point estimate falls from the parameter value given in the null hypothesis.

z-test

proportions(p)

t-test

means (Mu)

ANOVA test

comparison between 2 means

Chi-square test

correlations between categorical variables

p-values

is the probability that the test statistic takes the observed value or a value more extreme if we presume Ho is true

smaller p -values

represent stronger evidence against Ho

z-score

number of standard dev. from the mean

Confidence level

refers to the percentage of all possible samples that can be expected to include the true population parameter

Significance level

is the probability of rejecting a null hypothesis