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A company that sells its product on their website would like to improve the sales by making the webpage with product info more attractive. Current version (call it version A) and a new version (call it version B) are compared. A JavaScript code randomly chooses one of the two versions of the website to load to each customer that clicks on the link to the page about the product. Each version of the page has Buy button that leads the customer to purchase the product online. The company would like to test whether the new version (B) is better than the old one (A) by comparing the true probabilities pA and PB of purchasing the product for a randomly chosen visit of each website. Let Pд be probability that a randomly chosen visitor of website version A buys the product from the website. Similarly, let pg be the corresponding probability for version B. Let n₁ and n₂ be sample sizes of the visitors of versions A and B, respectively. Also, denote by X1 and X2 the numbers of visitors in the two X₁ samples who purchased the product, as well as sample proportions p and PB = n2 = X2 Part a) Which of the following tests can be used for this purpose? 1. Ho PA 2. Ho PA 3. Ho PA 4. Ho PA 5. Ho PA 6. Ho PA = = PB VS. Ha PA > PB: critical region: PA-PB >k for some k Є R. PB VS. Ha PA > PB: critical region: A-PR k for some k Є R. PB VS. Ha PA < PB; critical region: PA - PB k for some k Є R. PB VS. Ha PB: critical region: IPA-PB

A company that sells its product on their website would like to improve the sales by making the webpage with product info more attractive. Current version (call it version A) and a new version (call it version B) are compared. A JavaScript code randomly chooses one of the two versions of the website to load to each customer that clicks on the link to the page about the product. Each version of the page has Buy button that leads the customer to purchase the product online. The company would like to test whether the new version (B) is better than the old one (A) by comparing the true probabilities pA and PB of purchasing the product for a randomly chosen visit of each website. Let Pд be probability that a randomly chosen visitor of website version A buys the product from the website. Similarly, let pg be the corresponding probability for version B. Let n₁ and n₂ be sample sizes of the visitors of versions A and B, respectively. Also, denote by X1 and X2 the numbers of visitors in the two X₁ samples who purchased the product, as well as sample proportions p and PB = n2 = X2 Part a) Which of the following tests can be used for this purpose? 1. Ho PA 2. Ho PA 3. Ho PA 4. Ho PA 5. Ho PA 6. Ho PA = = PB VS. Ha PA > PB: critical region: PA-PB >k for some k Є R. PB VS. Ha PA > PB: critical region: A-PR k for some k Є R. PB VS. Ha PA < PB; critical region: PA - PB k for some k Є R. PB VS. Ha PB: critical region: IPA-PB

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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A company that sells its product on their website would like to improve the sales by making the webpage with product info more attractive. Current version (call it version A) and a new version (call it version B) are compared. A JavaScript code randomly chooses one of the two versions of the website to load to each customer that clicks on the link to the page about the product. Each version of the page has Buy button that leads the customer to purchase the product online. The company would like to test whether the new version (B) is better than the old one (A) by comparing the true probabilities pA and PB of purchasing the product for a randomly chosen visit of each website. Let Pд be probability that a randomly chosen visitor of website version A buys the product from the website. Similarly, let pg be the corresponding probability for version B. Let n₁ and n₂ be sample sizes of the visitors of versions A and B, respectively. Also, denote by X1 and X2 the numbers of visitors in the two X₁ samples who purchased the product, as well as sample proportions p and PB = n2 = X2 Part a) Which of the following tests can be used for this purpose? 1. Ho PA 2. Ho PA 3. Ho PA 4. Ho PA 5. Ho PA 6. Ho PA = = PB VS. Ha PA > PB: critical region: PA-PB >k for some k Є R. PB VS. Ha PA > PB: critical region: A-PR <k for some k Є R. PB VS. Ha PA <PR: critical region: PA-PB >k for some k Є R. PB VS. Ha PA < PB; critical region: PA - PB <k for some k Є R. PB vs. Ha PB: critical region: IPA-PR>k for some k Є R. PB VS. Ha PB: critical region: IPA-PB <k for some kЄ R. 7. None of the above PA PA
Transcribed Image Text:A company that sells its product on their website would like to improve the sales by making the webpage with product info more attractive. Current version (call it version A) and a new version (call it version B) are compared. A JavaScript code randomly chooses one of the two versions of the website to load to each customer that clicks on the link to the page about the product. Each version of the page has Buy button that leads the customer to purchase the product online. The company would like to test whether the new version (B) is better than the old one (A) by comparing the true probabilities pA and PB of purchasing the product for a randomly chosen visit of each website. Let Pд be probability that a randomly chosen visitor of website version A buys the product from the website. Similarly, let pg be the corresponding probability for version B. Let n₁ and n₂ be sample sizes of the visitors of versions A and B, respectively. Also, denote by X1 and X2 the numbers of visitors in the two X₁ samples who purchased the product, as well as sample proportions p and PB = n2 = X2 Part a) Which of the following tests can be used for this purpose? 1. Ho PA 2. Ho PA 3. Ho PA 4. Ho PA 5. Ho PA 6. Ho PA = = PB VS. Ha PA > PB: critical region: PA-PB >k for some k Є R. PB VS. Ha PA > PB: critical region: A-PR <k for some k Є R. PB VS. Ha PA <PR: critical region: PA-PB >k for some k Є R. PB VS. Ha PA < PB; critical region: PA - PB <k for some k Є R. PB vs. Ha PB: critical region: IPA-PR>k for some k Є R. PB VS. Ha PB: critical region: IPA-PB <k for some kЄ R. 7. None of the above PA PA
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