Download Introduction to Hypothesis tests with sigma known

Introduction to Hypothesis tests with sigma known A statistical hypothesis is a claim or assertion about 1. The value of a single parameter (describing the population probability distribution). 1.1. Example:   .75 , where  is the true average inside diameter of a certain kind of PVC pipe 2. The values of several parameters (sometimes comparing populations). 2.1. If 1 and  2 denote the true average breaking strengths of two different types of twine, the statement 1  2  0 represents the hypothesis that two breaking strengths are the same. 2.2. We do in this class 3. The form of an entire probability distribution. 3.1. Example: The distribution of chocolate bar weights is normal. 3.2. We don’t do in this class Null and alternative hypotheses In hypothesis testing problems, there are two contradictory hypotheses to be compared 1. The null hypothesis, denoted by H 0 , 1.1. Is the claim that is initially assumed to be true 1.2. The “prior belief” or “status quo” claim. 1.3. Is the hypothesis that allows us to calculate probabilities. 2. The alternative hypothesis, denoted by H a , or H1 , 2.1. Is the assertion that is contradictory to H 0 . 2.2. We will not reject the null hypothesis in favor of the alternative unless there is strong evidence in favor of the alternative. 2.3. Choose the alternative hypothesis so that a Type I error is the one with the worst real‐
life consequence (we’ll discuss these errors in a moment). Page 1 of 3 A ____________________ is a method for using __________________ to decide whether the null hypothesis_______________________. The null hypothesis will be rejected in favor of the alternative hypothesis only if sample evidence suggests that H 0 is false. 
If the sample does not strongly contradict H 0 , we will continue to believe in the plausibility of H 0 . The two possible inferences (conclusions) from a hypothesis‐testing analysis are 1. 2. General form of hypotheses, for a generic parameter  : Null: Alternative: 1. 2. 3. Example 1 of choosing null and alternative: Sometimes an investigator does not want to accept a particular assertion unless and until data can provide strong support for that assertion. Suppose a company is considering putting a new type of coating on bearings that it produces. The true average wear life with the current coating is known to be 1000 hours. With  denoting the true average life of the new coating, the company would not want to make a change unless evidence strongly suggested that  exceeds 1000. What should H 0 and H a be? Page 2 of 3 Example 2: Aspirin weight An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains. If the standard deviation is   .35 grains, does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Write the null and alternative hypotheses. How a hypothesis test works—using the aspirin example. 
If we saw a sample mean different from 5, o we would not immediately assume that the null hypothesis was wrong. o We know that due to sampling variability, even if the true mean were 5, our sample mean probably won’t be 5. 
If the sample mean were really far away from 5—in either direction, since the alternative is not equal to—then we would reject the null. o If the alternative is less than or greater than, we would only reject the null if the sample mean were far away from 0 . 
How far away must it be before we no longer believe 
To answer this, calculate the ________________. 
P‐value: H 0 ? Page 3 of 3