91Ó°ÊÓ

John has an online company that sells custom rims for cars and designed two different web pages that he wants to use to sell his rims online. However, he cannot decide which page to go with, so he decides to collect data to see which site results in a higher proportion of sales. He hires a firm that has the ability to randomly assign one of his two web page designs to potential customers. With web page design I, John secures a sale from 54 out of 523 hits to the page. With web page design II, John secures a sale from 62 out of 512 hits to the page. (a) What is the response variable in this study? What is the explanatory variable? (b) Based on these results, which web page, if any, should John go with? Why? Note: This problem is based on the type of research done by Adobe Test \& Target.

Step by step solution

01

Identify the Variables

The response variable is the outcome affected by the variables being studied. In this case, the response variable is the number of sales made. The explanatory variable is the condition that is manipulated to observe its effect on the response variable. Here, the explanatory variable is the web page design (design I or design II).

02

Calculate the Proportion of Sales for Each Web Page

For web page design I, the proportion of sales is calculated as follows: \ \[ p_1 = \frac{54}{523} \approx 0.1032 \] \ For web page design II, the proportion of sales is: \ \[ p_2 = \frac{62}{512} \approx 0.1211 \]

03

Compare the Proportions

Compare the proportions calculated in the previous step to determine which web page design resulted in a higher proportion of sales. \ \( p_1 \approx 0.1032 \) for design I and \( p_2 \approx 0.1211 \) for design II.

04

Conclusion

Design II has a higher proportion of sales (\( p_2 \approx 0.1211 \)) compared to design I (\( p_1 \approx 0.1032 \)). Therefore, John should go with web page design II as it results in a higher proportion of sales.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Response Variable

In any experiment or study, the response variable is the main factor being measured or observed. It is the outcome that researchers are interested in. In John's case, the response variable is the number of sales made on each web page. This variable shows how successful each web page design is in converting visitors into customers. By measuring the number of sales, John can determine which web page is more effective in driving sales for his custom rims.

Explanatory Variable

The explanatory variable is the one that is manipulated to observe its effect on the response variable. It helps explain changes in the response variable. In John's study, the explanatory variable is the web page design. John has two different designs (Design I and Design II) and wants to see which one performs better. By comparing the sales from both web page designs, John can understand the effect of the web page design on his sales.

Proportion Comparison

Making comparisons using proportions is a common method in statistical analysis. Proportions help us understand parts of a whole in a simplified form.
John calculates the proportion of sales for each web page design as follows:

• For Design I: The proportion of sales is \( p_1 = \frac{54}{523} \approx 0.1032 \)
• For Design II: The proportion of sales is \( p_2 = \frac{62}{512} \approx 0.1211 \)

Comparing these proportions allows John to see that Design II has a higher proportion of sales (\( p_2 \approx 0.1211 \)), indicating that it performs better in converting visitors into customers.

Web Page Design

Web page design plays a crucial role in user experience and conversion rates. A well-designed web page can attract visitors, encourage them to browse, and ultimately lead to a purchase. In John's experiment:

• Design I and Design II offer different layouts, styles, and user interfaces.
• These variations can influence how users interact with the site and make a purchase decision.

John's data collection aims to understand which design is more effective in driving sales. By analyzing sales data, he can make an informed decision on which design to use.

Sales Analysis

Analyzing sales performance is critical for any business looking to optimize its operations and improve profitability. In this study, sales analysis involves comparing the number of sales generated by each web page design.
John can perform this analysis through the following steps:

• Collecting sales data from both web page designs.
• Calculating the sales proportions for each design.
• Comparing these proportions to determine which design performs better.

Based on the results, Design II shows a higher proportion of sales, suggesting it is more effective. This targeted analysis helps John make better decisions for his business.