Background

TourisTopia Travel (Triple T) is an online travel agency that specializes in trips to exotic locations around the world for groups of ten or more travelers. Triple T’s marketing manager has been working on a major revision of the homepage of Triple T’s website. The content for the homepage has been selected and the only remaining decisions involve the selection of the background color (white, green, or pink) and the type of font (Arial, Calibri, or Tahoma).

Triple T’s IT group has designed prototype homepages featuring every combination of these background colors and fonts, and it has implemented computer code that will randomly direct each Triple T website visitor to one of these prototype homepages. For three weeks, the prototype homepage to which each visitor was directed and the amount of time in seconds spent at Triple T’s website during each visit were recorded. Ten visitors to each of the prototype homepages were then selected randomly; the complete data set for these visitors is available in the file *TourisTopia*.

Triple T wants to use these data to determine if the time spent by visitors to Triple T’s website differs by background color or font. It would also like to know if the time spent by visitors to the Triple T website differs by different combinations of background color and font.

** Do:**

In a managerial report,

- Use descriptive statistics to summarize the data from Triple T’s study. Based on descriptive statistics, what are your preliminary conclusions about whether the time spent by visitors to the Triple T website differs by background color or font? What are your preliminary conclusions about whether time spent by visitors to the Triple T website differs by different combinations of background color and font?
- Explain whether Triple T has used an observational study or a controlled experiment.
- Use the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three background colors. Include both factors and their interaction in the ANOVA model, and use a=.05. Please
**clearly****specify null and alternative hypothesis**in your post. - Use the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three fonts. Include both factors and their interaction in the ANOVA model, and use a=.05. Please
**clearly****specify null and alternative hypothesis**in your post. - Use the data from Triple T’s study to test the hypothesis that time spent by visitors to the Triple T website is equal for the nine combinations of background color and font. Include both factors and their interaction in the ANOVA model, and use a=.05. Please
**clearly****specify null and alternative hypothesis**in your post. - Discuss whether the results of your analysis of the data provide evidence that the time spent by visitors to the Triple T website differs by background color, font, or combination of background color and font. What is your recommendation?

**Discuss:**

- What recommendations does your ANOVA results support? Use findings from your managerial report to support your recommendations. Be sure to include why you support certain decisions over others. What surprising findings did you come up with during your analysis?

**Guided Response:** Review several of your peer’s posts. In a minimum of 100 words each, respond to at least two of your fellow students’ posts in a substantive manner, and provide information that they may have missed or may not have considered regarding the application of ANOVA tables in business and economics. Do you agree with their conclusions? Why or why not?

Post by classmate 1

Hello Class

**Use descriptive statistics to summarize the data from Triple T’s study. Based on descriptive statistics, what are your preliminary conclusions about whether the time spent by visitors to the Triple T website differs by background color or font? What are your preliminary conclusions about whether time spent by visitors to the Triple T website differs by different combinations of background color and font?**

The descriptive statistics show that the white background and Arial font combination will generate the biggest average time spent by customers on the website. Meanwhile, the pink background with Tahoma font is the least popular by the customers.

**Explain whether Triple T has used an observational study or a controlled experiment.**

Triple T used a controlled method for this experiment. They manually used different combinations of fonts and background colors and then measured them.

**Use the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three background colors. Include both factors and their interaction in the ANOVA model, and use a=.05. Please clearly specify null and alternative hypothesis in your post.**

The null hypothesis is that there is no significant differences between the backgrounds. The alternative hypothesis will show at least one significant difference between the backgrounds. If the P-value associated with the F is smaller than .05 then the null hypothesis is rejected and the alternative hypothesis is supported. The data provided shows that the F value is 5.749643 and the P-value is 0.004624. Since this value is smaller than .05, the null hypothesis is rejected.

**Use the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three fonts. Include both factors and their interaction in the ANOVA model, and use a=.05.**

The null hypothesis is that there are no significant differences between the fonts. The alternative hypothesis will show at least one significant difference among the fonts. The data shows that the mean time spent on the website by visitors is for the 3 fonts is .00676. Since the P-value associated with the F-value is smaller than .05, the null hypothesis is rejected.

**Use the data from Triple T’s study to test the hypothesis that time spent by visitors to the Triple T website is equal for the nine combinations of background color and font. Include both factors and their interaction in the ANOVA model, and use a=.05. Please clearly specify null and alternative hypothesis in your post.**

The null hypothesis is that there are no significant differences in time spent. The alternative hypothesis will show at least one significant difference among the combinations. The interaction test between the background color and font is 0.2269. Since the P-value associated with the F-value is smaller than .05, the null hypothesis is rejected.

**Discuss whether the results of your analysis of the data provide evidence that the time spent by visitors to the Triple T website differs by background color, font, or combination of background color and font. What is your recommendation?**

For the 9 combinations, that data concludes that visitors to the white background and Aria font spend more time 310.4 on the website. The sample data also suggests that the variance for the white background and Tahoma font 339.1667 is smaller than the other variance combinations. The final recommendation is that the company Triple T should adopt the white background and Arial font prototype

Post by classmate 2

Attached are the results for the ANOVA: Two-Factor with Replication statistics for the Data File TourisTopia. ANOVA is a statistical method that tests the null hypothesis that given populations have the same mean by comparing the variability between groups to the variability within groups; and the F test statistic (or F-value) is what enables us to find the p-value to support or reject the hypothesis (Jbstatistics, n.d.). In summary of this data, I have concluded that customers within the case study spent more time on the website prototypes that utilized a white background and an Arial font. The website prototypes that utilized a pink background with a Tahoma font resulted in the least amount of time spent by customers. The data suggests that both background color and font are significant, but the interaction between background color and font is not.

TourisTopia Travel (Triple T) has utilized a controlled experiment to obtain this data. It had designed prototype homepages with variations of background colors and font types and randomly directed customers to each site to generate the data needed (Anderson et al., 2021).

A null hypothesis for an ANOVA assumes there are no significant differences between the groups, and the alternative hypothesis assumes at least one significant difference (University of Arizona Global Campus, 2020). Utilizing the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three background colors, my null hypothesis is that there would be no difference between time spent. My alternative hypothesis is that more time would be spent on one color background as opposed to the others. The F-value of the sample data is 5.7496, with a P-value of 0.0046. Since the P-value associated with the F-value is smaller than .05, the null hypothesis is rejected, and the alternative hypothesis is supported.

Utilizing the data from Triple T’s study to test the hypothesis that the time spent by visitors to the Triple T website is equal for the three fonts, my null hypothesis is that there would be no difference between time spent. My alternative hypothesis is that more time would be spent on one font as opposed to the others. The F-value of the sample data is 5.3180, with a P-value of 0.0067. Since the P-value associated with the F-value is smaller than .05, the null hypothesis is rejected, and the alternative hypothesis is supported.

Utilizing the data from Triple T’s study to test the hypothesis that time spent by visitors to the Triple T website is equal for the nine combinations of background color and font, my null hypothesis is that there would be no difference in time spent. My alternative hypothesis is that more time would be spent with one or more combinations of color and font. The F-value of the interaction data is 1.444, with a P-value of 0.2269. Since the P-value associated with the F-value is larger than .05, the null hypothesis is supported, and the alternative hypothesis is rejected.

Data suggests that visitors to the white background prototype spent more time at the website, as did the visitors to the Arial font prototype website (University of Arizona Global Campus, 2020). Given the results of the data, the background color is significant, and the font is significant, but the interaction between the background color and font is not significant (University of Arizona Global Campus, 2020). My recommendation for Triple T would be to utilize the website with the white background and Ariel font as the data supports customers spending more time on the sites with these options. I discovered in the data analysis that when the F-value was greater than the F-critical value, it also suggested the rejection of the null hypothesis. In contrast, when the F-value was greater than the F-critical value, it suggested a failure to reject the null hypothesis.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., & Ohlmann. J. W. (2021). __ Essentials of modern business statistics with Microsoft® Excel®__ (8th ed.). Cengage Learning

Jbstatistics. (n.d.). *Introduction to One-Way ANOVA.* https://www.youtube.com/watch?v=QUQ6YppWCeg

University of Arizona Global Campus. (2020, September 11). *Week 4 introduction* [Video]. Kaltura. https://ashford.mediaspace.kaltura.com/media/BUS308+%7C+Week+4+Introduction/1_9dibo9bq