Additional Topics Regarding Hypothesis Testing

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Presentation transcript:

Additional Topics Regarding Hypothesis Testing Sec 8.6 Additional Topics Regarding Hypothesis Testing Bluman, Chapter 8

8.6 Additional Topics Regarding Hypothesis Testing There is a relationship between confidence intervals and hypothesis testing. When the null hypothesis is rejected in a hypothesis-testing situation, the confidence interval for the mean using the same level of significance will not contain the hypothesized mean. Likewise, when the null hypothesis is not rejected, the confidence interval computed using the same level of significance will contain the hypothesized mean. Bluman, Chapter 8

Chapter 8 Hypothesis Testing Section 8-6 Example 8-30 Page #450 Bluman, Chapter 8

Example 8-30: Sugar Production Sugar is packed in 5-pound bags. An inspector suspects the bags may not contain 5 pounds. A sample of 50 bags produces a mean of 4.6 pounds and a standard deviation of 0.7 pound. Is there enough evidence to conclude that the bags do not contain 5 pounds as stated at α = 0.05? Also, find the 95% confidence interval of the true mean. Step 1: State the hypotheses and identify the claim. H0: μ = 5 and H1: μ  5 (claim) Step 2: Find the critical value. The critical values are z = ±1.96. Bluman, Chapter 8

Example 8-30: Sugar Production Sugar is packed in 5-pound bags. An inspector suspects the bags may not contain 5 pounds. A sample of 50 bags produces a mean of 4.6 pounds and a standard deviation of 0.7 pound. Is there enough evidence to conclude that the bags do not contain 5 pounds as stated at α = 0.05? Also, find the 95% confidence interval of the true mean. Step 3: Compute the test value. Bluman, Chapter 8

Example 8-30: Sugar Production Step 4: Make the decision. Reject the null hypothesis. Step 5: Summarize the results. There is enough evidence to support the claim that the bags do not weigh 5 pounds. Bluman, Chapter 8

Example 8-30: Sugar Production The 95% confidence interval for the mean is 4.401<μ<4.800 Notice that the 95% confidence interval of mean does not contain the hypothesized value μ = 5. Hence, there is agreement between the hypothesis test and the confidence interval. Bluman, Chapter 8

Example 8-31 A researcher claims that adult hogs fed a special diet will have an average weight of 200 pounds. A sample of 10 hogs has an average weight of 198.2 pounds and a standard deviation of 3.3 pounds. At a=0.05, can the claim be rejected? Reconcile your conclusion with the 95% CI of the true mean. Bluman, Chapter 8

On your own Read pages 459-460. Do exercises 8-6 Page 461 # 1,3,5 Bluman, Chapter 8

Power of a Statistical Test The power of a test measures the sensitivity of the test to detect a real difference in parameters if one actually exists. The higher the power, the more sensitive the test. The power is 1 – β. Bluman, Chapter 8