Nefarian just landed his first data science position as an intern at a new e-commerce company. His project was the design and test a new website layout that would lead to more purchases. To test his new layout, the company gathered four different groups of 20 customers and recorded how many of those ended up purchasing an item. This test was then repeated on multiple days. The effectiveness of Nefarian's layout is measured by the number of customers that made a purchase. This data is stored in the data frame purchases.

Nefarian wants to land a permanent position at the company after his internship is over, so he really wants to impress his supervisors with his new layout. He knows that the site has an average purchase rate of 0.8 and wants to see if his layout is an improvement.

Part A) Use the entire dataset to determine whether Nefarian's layout is an improvement over the original layout.

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Use an appropriate hypothesis test and a significance level of =0.05. Find the p-value for this test.

Part B) Based on your results from Part A, is Nefarian's layout an improvement over the original layout?