Chapter 9

two-tailed hypothesis test

A test in which the null hypothesis can be rejected on either side of the hypothesized value of the population parameter

one-tailed hypothesis test

A test in which the null hypothesis is rejected only on one side of the hypothesized value of the population parameter

four-step procedure using the p-value Step 3.

Calculate the value of the test statistic and the p-value

alternative hypothesis HA

In a hypothesis test, the alternative hypothesis contradicts the default state or status quo specified in the null hypothesis. Generally, whatever we wish to establish is placed in the alternative hypothesis

null Hypothesis HO

In a hypothesis test, the null hypothesis corresponds to a presumed default state nature or status quo.

type II error

In a hypothesis test, this error occurs when the decision is to not reject the null hypothesis when the null hypothesis is actually false

left-tailed test

In hypothesis testing, when the null hypothesis is rejected if the value of the test statistic falls in the left tail of the distribution

right-tailed test

In hypothesis testing, when the null hypothesis is rejected if the value of the test statistic falls in the right tail of the distribution

we follow three steps when formulating the competing hypothesis

1) Identify the relevant population parameter or interest 2) Determine whether it is a one- or two-tailed test 3) Include some form of equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

four-step procedure using the p-value approach Step 1.

Specify the null and alternative hypotheses

four-step procedure using the p-value approach Step 2.

Specify the significance level

four-step procedure using the p-value approach step 4.

State the conclusion and interpret results

test statistic

a sample-based measure used in hypothesis testing

type I error

in a hypothesis test, this error occurs when the decisions is to reject the null hypothesis when the null hypothesis is actually true

significance level

the allowed probability of making a type 1 error as alpha

when using the p-value approach

the decision rule is to reject the null hypothesis if the p-value < alpha and not reject the hypothesis if the p-vale is >=alpha

p-value

the likelihood of obtaining a sample mean that is at least extreme as the one derived from the given sample, under that assumption that the null hypothesis is true as an equality/ referred to as the observed probability of making a type 1 error

test statistic for mu when sigma is known

the value of the test statistic for the hypothesis test of the population mean mu when the population standard deviation sigma is know and computed as... where mu0 is the hypothesized value of the population mean. This value is ONLY valid if xbar approximately follows a NORMAL DISTRIBUTION

test statistic for mu when sigma is unknown

the value of the test statistic for the hypothesis test of the population mean mu when the population standard deviation sigma is unknown is computed as where m0 is the hypothesized value of the population mean and the degrees of freedom df=n-1. this formula is valid only if xbar is (approximately) follows a normal distribution.

if the null hypothesis if rejected at 1% significance level

then the null hypothesis is rejected at a 5% significance level

if the chosen significance level alpha = .05 then

there is a 5% chance of rejecting a true hypothesis

the p-value approach

under the assumption that mu=m0, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample. Its calculation depends on the specification of the alternative hypothesis. The decision rule: Reject H0 is the p-value <alpha

population mean

μ; the complete collection of items in a statistical problem