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
