3 goal of the process is to determine whether there is enough evidence to infer

# 3 goal of the process is to determine whether there

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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 o 4) there are two possible decisions: conclude that there is enough evidence to support the alternative hypothesis conclude that there is not enough evidence to support the alternative hypothesis o 5) two possible errors can be made in any test. A type 1 error occurs when we reject a true null hypothesis P(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 H 0 will always state that the parameter equals the value specified in the alternative hypothesis H 1 Example- computer company wants to look at inventory levels at outside warehouses Manager wants to know whether the mean is different from 350 units Test hypothesis is H 0 : = 350 Research hypothesis is H 1: ≠ 350 Testing begins with assuming the null hypothesis is true, until we have further statistical evidence we will assume. Ie we assume H 0 : = 350 is true Goal 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? H 1: ≠ 350 which is what we are interested to know. There are 2 possible decisions that can be made: o Conclude that there is enough evidence to support the alternative hypothesis (also stated as rejecting the null hypothesis in favor of the alternative) o Conclude 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 350 Two possible errors can be made in any test: o Type I error occurs when we reject a true null hypothesis o Type II error occurs when we don’t reject a false null hypothesis P(Type I error)= Probability of denoted by also called the significance level P(Type II error)= Types of errors Type I error occurs when we reject a true null hypothesis o Reject H 0 when it is true Type II error occurs when we don’t reject a false null hypothesis
o Do not reject H 0 when it is false Testing the population mean when the population standard deviation is know Example- department store manager is considering new billing system. After financial analysis she