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Feb 20, 2024

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Name: _Ryan DiStefano______________________ Chapter 6 Flipped Notes Mr. Reid’s Video 6.1-HT: Hypothesis Tests by Hand for a Population Proportion This approach assumes we have an approximately normal sample proportion – based on the Z (Standard Normal Curve). The basic process (assuming we do have a normal sample proportion). 1. Think about the hypotheses: Use appropriate notation to jot them down. 2. Standardize the sample proportion applying the z-score formula: This gives you the “test statistic”. Formula: 1. Find the p-value. I always include a sketch to visualize it. We will use either normal area tables, or StatKey to find the p-value. 2. Figure out the conclusion and then write it in the context of the problem. Example 1 A quality control process includes a step where manufactured items are inspected for cosmetic defects. The baseline that has been established over time is that at this stage 9% of the items have a defect and need to be touched up before being packaged for sale. Periodically the manager samples random batches of items to test to see if there is evidence that the population proportion of items with cosmetic defects has increased from 9%. She uses 5% significance level. In the last sampled batch there were 250 items and 37 had cosmetic defects. Conduct the appropriate hypothesis test showing: A. The Hypotheses B. The Test Statistic C. The P-value D. The Conclusion Work for Example 1:

A possible error? Every time we do a hypothesis test there is a chance of making an error. For this test we ended up rejecting the null hypothesis in favor of the alternative. We could have made a type I error. This happens when: we have strong enough evidence to reject the null hypothesis when the null was actually true How likely is this? Alpha (the significance level) gives the probability of a type I error Example 2: Support for the legalization of marijuana was studied a short time ago in a small city. The best guess for the population proportion of adults in that city who support legalization was 58%. Suppose a new study is being done to see if there was significant evidence to claim the level of support had changed. To do this, a random sample of 300 adults in that city were sampled and 56% of them favored legalization. Conduct the appropriate hypothesis test at the 10% significance level. Example 2 Work:

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