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3) goal of the process is to determine whether there is enough evidence to infer that the alternative hypothesis is true o4) there are two possible decisions:conclude that there is enough evidence to support the alternative hypothesisconclude that there is not enough evidence to support the alternative hypothesiso5) two possible errors can be made in any test. A type 1 error occurs when we reject a true null hypothesisP(Type I error)= A type II error occurs when we don’t reject a false null hypothesis (ie accept but don’t say that) P(Type II error)= Critical concepts in Hypothesis testing: Concept 1 -The null hypothesis H0will always state that the parameter equals the value specified in the alternative hypothesis H1Example- computer company wants to look at inventory levels at outside warehouses Manager wants to know whether the mean is different from 350 unitsTest hypothesis is H0: = 350Research hypothesis is H1:≠ 350Testing begins with assuming the null hypothesis is true, until we have further statistical evidence we will assume. Ie we assume H0: = 350 is trueGoal of the process is to determine whether there is enough evidence to infer that the alternative hypothesis is true.. Is there statistical evidence to determine if this statement is true? H1:≠ 350 which is what we are interested to know.There are 2 possible decisions that can be made:oConclude that there is enough evidence to support the alternative hypothesis (also stated asrejecting the null hypothesis in favor of the alternative)oConclude that there is not enough evidence to support the alternative hypothesis (also stated as not rejecting the null hypothesis in favor of the alternative) Note we DO NOT say we accept the null hypothesis (although this is what it means we are doing)Once the null and alternative hypothesis are stated, the next step is to randomly sample the population and calculate the test statistic (in this example the sample mean)If the test statistic value is inconsistent with the null hypothesis, we reject the null hypothesis and infer the alternative hypothesis is true. For example if we are trying to decide if the mean is not equal to 350, a large value of x, say 600, would provide enough evidence. If x is close to 350 say 355, we could not say that this provides a great deal of evidence to infer that the population mean is different that 350Two possible errors can be made in any test: oType I error occurs when we reject a true null hypothesisoType II error occurs when we don’t reject a false null hypothesisP(Type I error)= Probability of denoted by also called the significance levelP(Type II error)= Types of errorsType I error occurs when we reject a true null hypothesisoReject H0when it is trueType II error occurs when we don’t reject a false null hypothesis
oDo not reject H0when it is falseTesting the population mean when the population standard deviation is knowExample- department store manager is considering new billing system. After financial analysis she