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- Describe the 8 steps in the process for hypothesis testing.Explain the decision criteria for rejecting the null hypothesis for both the p-value method and the critical value method.
Answer and Explanation:
In hypothesis testing, the first step is to identify the claim to be tested. Step number two is to give the symbolic form that must be true when the original claim is false. This step is when you establish your alternative hypothesis and can determine if it is true or not. Step 3 is to identify the Null and Alternative Hypothesis. These are identified by using Ho for the null hypothesis and H1 or Hafor the alternative hypothesis. Step 4 is selecting the significance level. The significance level is represented by α (alpha) during hypothesis testing. This is also known as the confidence level. Step 5 is identifying the test statistic. There are two different test statistics’, z-score and t-statistic. The Z-score (z) is used when sigma, population standard deviation (σ) is known (this is uncommon). The t-statistic () will be used when the standard deviation (σ) sigma is not known. Next is step number six, in this step, you will determine if you should reject the null hypothesis or not. In determining if the null hypothesis should be rejected or not you can use either the p-value method or the critical value method. The p-value method you are finding the probability of the test statistic whereas the critical value method is determiningwhere the rejection region begins and then compares the test statistic to that number. There are two types of test, one-tailed and two-tailed. Step number seven is where you decide to either reject the null hypothesis or not. If you used the p-value, you would reject (Ho) if the p-value is less than or equal to the significance level (p-value ≤ α) or you will fail to reject Ho if the p-value is greater than the significance level (p-value > α). You should get the same result with both methods. The final step in hypothesis testing is to come to a conclusion and restate the decision in nontechnical terms by noting that there is either sufficient evidence to support or to reject the claim in your test.
The remaining problems refer to the following scenario:
A claim is made that the average salary for all jobs in Minnesota is less than $75,000. You are going to test the claim using and assume that your data is normally distributed and the population standard deviation is not known.