AP Statistics homework_Chapter20 Name_ The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A marketing salesman suggests that she invest in a new line of celebrity mannequins (think Seth Rogan modeling the latest jeans...). He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll purchase the mannequins. She'll buy the mannequins if there is evidence that the percentage of people that buy something increases. 1. Write the owner's null and alternative hypotheses. 2. In this context describe a Type I error and the impact such an error would have on the store. 3. In this context describe a Type II error and the impact such an error would have on the store. 4. Based on data that she collected during the trial period the store's owner found that a 98% confidence interval for the proportion of all shoppers who might buy something was (27%, 35%). What conclusion should she reach about the mannequins? Explain. 5. What alpha level did the store's owner use? 6. Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead. 7. The owner talked the salesman into extending the trial period so that she can base her decision on data for a full month. Will the power of the test increase, decrease, or remain the same? 8. Over the trial month the rate of in-store sales rose to 30% of shoppers. The store's owner decided this increase was statistically significant. Now that she's convinced the mannequins work, why might she still chose not to purchase them? 1/2