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.

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.

Case Study: Touris Topia Travel 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. 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 Managerial Report Prepare a managerial report that analyzes the collected data and makes a recommendation to TourisTopia about the background color and type of font to use on the homepage. Given Data Ten visitors to each of the prototype homepages were selected randomly; consider the complete data set for these visitors, TourisTopia. A B C D E F G H I J K Ariel Calibri Tahoma white background 301 225 217 288 250 259 234 173 234 381 267 270 295 356 245 351 253 239 298 230 268 290 261 245 311 294 273 355 216 265 green background 275 258 261 271 216 193 210 203 280 324 223 282 327 159 227 200 178 217 257 241 180 266 312 285 205 310 254 194 310 313 pink background 209 251 201 292 273 247 261 269 188 247 121 198 259 344 221 284 224 204 161 181 208 291 252 256 205 181 174 323 253 167Descriptive Statistics Calculate the mean (in seconds) and variance for the amount of time visitors spent at Triple T's website for each background color and font. (Round your answers to two decimal places.) Mean Variance White Color Green Pink Arial Font Calibri Tahoma What preliminary conclusions can be drawn based on only the background color and font used? When font is ignored, the sample data suggest that visitors spent the most time at the Triple T website when the background color was --Select-- When background color is ignored, the sample data suggest that visitors spent the most time at the Triple T website with the font -Select-- v]. Calculate the mean (in seconds) and variance for the amount of time visitors spent at Triple T's website for each background color and font combination, (Round your answers to two decimal places.) Font Background Color Arial Calibri Tahoma Mean White Variance Mean Green Variance Mean Pink Variance What preliminary conclusions can be drawn based on the background color and font combinations used? Visitors spent the most amount of time on the website when the background color was |-Select-- |and the font used was |-Select-- v. Visitors spent the least amount of time on the website when the background color was | - Select . |and the font used was [- Select-.w]. Study or Experiment? Has Triple T used an observational study or a controlled experiment? Explain. Since the prototypes featuring the three background colors and the three fonts to visitors [--Select--| randomly assigned, Triple T used [-Select-- Hypothesis Test-Background Color 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 i = 0.05. (You may need to use the appropriate technology to answer this question.) State the null and alternative hypotheses. O Ho: Not all population means are equal. Ha! Awhite = /green = P pink O Hot #white * Agroon * "pink Ha! Awhite = /green = Ppink O Ho: Awhite = "green = pink H: Not all population means are equal Ho: "white = /green = #pink Hai "white * #green * "pink Find the value of the test statistic. (Round your answer to two decimal places. ) 5.75 Find the p-value. (Round your answer to four decimal places.) 0.005 State your conclusion. Because the p-value is less than or equal to w | 0.05, the background color is not |significant.Hypothesis Test-Font 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 = 0.05. (You may need to use the appropriate technology to answer this question.) State the null and alternative hypotheses. Ho- Marial = /callbri = MTahoma Wai Marial * /Callori * #Tahoma He: Marial = /calibri = Tahoma He: Not all population means are equal. O Ho: Marial * #calibri * "Tahoma Ha! Marial = Acalibri = /Tahoma He: Not all population means are equal. Hai Marial " "calibri " "Tahoma Find the value of the test statistic. (Round your answer to two decimal places.) 5.32 Find the p-value. (Round your answer to four decimal places.) 0.007 State your conclusion. Because the p-value is |loss than or equal to w | 0.05, the font is not |significant. Hypothesis Test-Interaction Use the data from Triple T's study to test the hypothesis that the interaction between background color and font has a significant impact on the time spent by visitors. Include both factors and their interaction in the ANOVA model, and use a = 0.05. (You may need to use the appropriate technology to answer this question.) Find the value of the test statistic. (Round your answer to two decimal places.] 1.44 Find the p-value. (Round your answer to four decimal places.) 0.227 State your conclusion. Because the p-value is | greater than | 0.05, the interaction |is * significant. Recommendation Do 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? The results of the analysis of variance suggest that there --Select-- |differences between the three background colors in the mean time spent by visitors to the Triple T website. The results of the analysis of variance suggest that there |- Select- |differences between the three fonts in the mean time spent by visitors. The descriptive statistics suggest that the greatest mean time spent by visitors to the Triple T website occurs for the |--Select--| background and the [- Select-- w| font. What is your recommendation based on the results of the hypothesis test and descriptive statistics? (Select all that apply.) () white background O green background O pink background O Arial font O Calibri font Tahoma font Neither the background color nor the font were found to be significant