Formulating the Hypothesis null hypothesis 4 The null hypothesis is a statement about the population value that will be tested. null hypothesis 4 The null hypothesis will be rejected only if the sample data provide substantial contradictory evidence.

Formulating the Hypothesis alternativehypothesis 4 The alternative hypothesis is the hypothesis that includes all population values not covered by the null hypothesis. alternative hypothesis 4 The alternative hypothesis is deemed to be true if the null hypothesis is rejected.

Formulating the Hypothesis research hypothesis alternativehypothesis The research hypothesis (usually the alternative hypothesis ): 4 Decision maker attempts to demonstrate it to be true. 4 Deemed to be the most important to the decision maker. 4 Not declared true unless the sample data strongly indicates that it is true.

Types of Statistical Errors 4 Type I Error 4 Type I Error - This type of statistical error occurs when the null hypothesis is true and is rejected. 4 Type II Error 4 Type II Error - This type of statistical error occurs when the null hypothesis is false and is not rejected.

Types of Statistical Errors

Establishing the Decision Rule critical value The critical value is 4 Determined by the significance level. 4 The cutoff value for a test statistic that leads to either rejecting or not rejecting the null hypothesis.

Establishing the Decision Rule significance level The significance level is the maximum probability of committing a Type I statistical error. The probability is denoted by the symbol .

Reject H 0 Do not reject H 0 Sampling Distribution Maximum probability of committing a Type I error =  Establishing the Decision Rule (Figure 8-3)

Rejection region  = From the standard normal table Then Establishing the Critical Value as a z -Value

Establishing the Decision Rule test statistic The test statistic is a function of the sampled observations that provides a basis for testing a statistical hypothesis.

Rejection region  = Test Statistic in the Rejection Region

Establishing the Decision Rule p-value The p-value is 4 The probability of obtaining a test statistic at least as extreme as the test statistic we calculated from the sample. 4 Also known as the observed significance level.

Rejection region  = Relationship Between the p- Value and the Rejection Region p-value =

Using the p-Value to Conduct the Hypothesis Test p-value is less than or equal to a 4If the p-value is less than or equal to a, reject the null hypothesis. p-value is greater than a 4If the p-value is greater than a, do not reject the null hypothesis. Example: For  = 0.05 with the p-value = 0.02 for a particular test, then the null hypothesis is rejected.

One-Tailed Hypothesis Tests one-tailed hypothesis test A one-tailed hypothesis test is a test in which the entire rejection region is located in one tail of the test statistic’s distribution.

Two-Tailed Hypothesis Tests two-tailed hypothesis test A two-tailed hypothesis test is a test in which the rejection region is split between the two tails of the test statistic’s distribution.

0 Two-Tailed Hypothesis Tests (Figure 8-7)

When  Is Unknown 4The sample standard deviation is used. 4The test statistic is calculated as 4The critical value is found from the t-table (Appendix F) using n-1 degrees of freedom.