sta 215 chapter 17

steps for carrying out a significance test

1.state the null and alternative hypotheses, as well as the significance level 2. check the assumptions and calculate the test statistic 3. calculate the p-value 4. state your conclusion in the context of the problem

null hypothesis and alternative hypothesis

a hypothesis has two tests

alternative hypothesis

denoted Ha, is a hypothesis to be considered as an alternative to the null hypothesis

null hypothesis

denoted h0, is a hypothesis to be tested. We will consider this to be true until it is proven falso.

p-value

denoted p, of a hypothesis test is the probability of getting sample data at least as inconsistent with the null hypothesis (and supportive of the alternative hypothesis) as the sample data actually obtained. p is small, get rid of the Ho

reasoning of tests of significance (hypothesis tests)

how likely would it be to see the results we saw if the claim of the test were true? do the data give evidence against the claim?

hypothesis test

involves deciding whether the null hypothesis should be rejected in favor of the alternative hypothesis

hypothesis

is a statement that something is true. ( in reality, this something may or may not be true)

test statistic

is a statistic calculated from the sample data

type II error

is the error of not rejecting the null hypothesis when its actually false

type I error

is the error of rejecting the null hypothesis when its actually true

basic logic of hypothesis testing

take a random sample from the population. If the sample data are consistent with the null hypothesis, do not reject the null hypothesis; if the sample data are not consistent with the null hypothesis, but instead support the alternative hypothesis, then reject the null hypothesis in favor of the alternative hypothesis. because our decision about the population is based on a sample, it's possible we could make the wrong decision

guidelines for choosing the hypotheses

the null hypothesis for a hypothesis test concerning a population mean, mu, will always be that mu is equal to some hypothesized value, mu0. in symbols, that is mu=mu0 the choice of the alternative hypothesis depends on, and should reflect, the purpose of the hypothesis test. Three choices are possible for the alternative hypothesis: mu not equal mu0, mu> mu0, or mu<m0 The alternative hypothesis is one-tailed or one-sided if it states that a parameter is larger than or smaller than the null hypothesis value (so the test may be called right-tailed or left-tailed respectively). IT is two-tailed (or two-sided) if it states that the parameter is different than not equal to the null value

determining a p-value

to determine the p-value of a hypothesis test, first assume the null hypothesis is true. Then compute the probability of observing a test statistic at least as extreme as the one actually observed.

possible conclusions for a hypothesis test

to reach a conclusion, we compare the p-value to some pre-determine level of significance. we can choose the significance level for our hypothesis test. * if the p-value is less than or equal to the specified significance level, then reject the null hypothesis; otherwise do not reject the null hypothesis. in other words, reject ho is p< x otherwise do not reject ho *if the null hypothesis is rejected, we conclude that the data provide sufficient evidence to support the alternative hypothesis. in this case, or results are statistically significant at the the x level- enough evidence to say no if the null hypothesis is not rejected, we conclude that the data do not provide sufficient evidence to support the alternative hypothesis. in this case, or results are not statistically significant at the x level