Lecture07

# Lecture07 - Hypotheses Null Hypothesis claims that the...

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Hypotheses Null Hypothesis – claims that the effect we are looking for does not exist. It is the “no change” or “no difference” hypothesis. Alternative Hypothesis – claims that the effect we are looking for does exist. General Hypotheses Two-tailed Hypotheses H 0 : μ = k H a : μ ! k One-tailed Hypotheses (left and right tailed) H 0 : μ = k H a : μ < k or H a : μ > k Information The null hyp. (H 0 ) is assumed to be true throughout the statistical analysis. Only if the sample observations are in extreme contradiction to H 0 do we reject H 0 in favor of H a . If H 0 cannot be rejected, we do not conclude that H 0 is true but merely that we have no evidence to reject it. What can happen After stating the hypothesis we will run the test Two possibilities: 1) H 0 is true, the difference between the sample mean and the population mean is due to chance. 2) H 0 is false, the sample came from a population whose mean is not the same.

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What can happen But there are actually four outcomes (two are correct). A null hypothesis may or not be true, and a decision is made to reject or not reject it. Four outcomes H 0 is true H 0 is false Reject H 0 Type I error Correct Don’t reject H 0 Correct Type II error Type I error occurs if one rejects a true H 0 Type II error occurs if one does not reject H 0 when it is false. Example Defendant – is innocent or not innocent but will either be convicted or acquitted. H 0 : defendant is innocent H a : defendant is not innocent Type I error – convicted when innocent Type II error – acquitted when not innocent Error P(Type I error) = ! . This is called the significance level. P(Type II error) = # . ! and # are inversely related. Any attempt to reduce one will increase the other.
Significance Level Typical values for ! are .10, .05, and .01. If the null hypothesis is rejected, the probability of type I error will be 10%, 5% or 1%. ! = .10 , there is a 10% chance of rejecting a true null hyp. ! = .05, there is a 5% chance of rejecting a true null hyp. Test Statistic Measures compatibility between the null hypothesis and the data. Used for the probability calculation needed for our hypothesis test. Here we use the z test statistic. Steps to solve a hypothesis test 1) State the hypotheses 2) Determine the significance level (given or chosen) 3) Calculate the test statistic 4) Make a decision to reject or not reject the null hypothesis 5) Draw conclusions and interpret results. Reject or Not Reject Two approaches to making a decision after the test statistic is calculated. 1) Rejection Region Approach 2) P-Value Approach We will learn both and we will use both in our problems. One will always verify the other.

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Rejection Region Terms: Critical Value – separates the rejection region from the non-rejection region. Rejection Region
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Lecture07 - Hypotheses Null Hypothesis claims that the...

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