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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. a) Write the owner's null and alternative hypotheses. b) In this context describe a Type I error and the impact such an error would have on the store. c) In this context describe a Type II error and the impact such an error would have on the store. d) 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. e) What alpha level did the store's owner use? f) Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead. g) 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?

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. a) Write the owner's null and alternative hypotheses. b) In this context describe a Type I error and the impact such an error would have on the store. c) In this context describe a Type II error and the impact such an error would have on the store. d) 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. e) What alpha level did the store's owner use? f) Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead. g) 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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. a) Write the owner's null and alternative hypotheses. b) In this context describe a Type I error and the impact such an error would have on the store. c) In this context describe a Type II error and the impact such an error would have on the store. d) 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. e) What alpha level did the store's owner use? f) Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead. g) 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?
Transcribed Image Text: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. a) Write the owner's null and alternative hypotheses. b) In this context describe a Type I error and the impact such an error would have on the store. c) In this context describe a Type II error and the impact such an error would have on the store. d) 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. e) What alpha level did the store's owner use? f) Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead. g) 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?
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