As T.C. Resort Properties seeks to improve its customer service, the company faces new competition from SunLow Resorts. SunLow has recently opened resort hotels on the islands where T.C. Resort Properties has its five hotels. SunLow is currently advertising that a random survey of 300 customers revealed that about 60% of the customers preferred its “Concierge Class” travel reward program over the T.C. Resorts “TCRewards Plus” program.

Open and review ConciergeClass.pdf, an electronic brochure that describes the Concierge Class program and compares it to the T.C. Resorts program. Then answer the following question:

What analyses of the survey data would lead to a more favorable impression about T.C. Resort Properties?

Who uses a cellphone while watching TV? The Pew Research Center’s Internet and American Life Project measured the prevalence of multiscreen viewing experiences by asking American adults who are cellphone owners whether they had used their phone to engage in several activities while watching TV. The study reported that 171 of 316 (54%) of urban American cellphone owners sampled, 516 of 993 (52%) of suburban American cellphone owners sampled, and 251 of 557 (45%) of rural American cellphone owners used their phone to engage in several activities while watching TV.

a. Is there evidence of a significant difference among the urban, suburban, and rural American cellphone owners with respect to the proportion who use their phone to engage in several activities while watching TV? (Use $\alpha = 0.05$).

b. Determine the p-value and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha = 0.05$ to determine which groups differ.

The MSCI 2016 Survey of Women on Boards Survey showed that there continues to be a slow increase in the overall percentage of women on boards globally. The study reported that 69 of 70 (99%) French companies sampled, 39 of 53 (74%) German companies sampled, 8 of 22 (36%) Irish companies, 15 of 24 (63%) Spanish companies, and 12 of 42 (29%) Swiss companies sampled have at least three female directors on their boards.

a. Is there evidence of a significant difference among the countries with respect to the proportion of companies who have at least three female directors on their boards? (Use $\alpha$ = 0.05).

b. Determine the p-value and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha$ = 0.05 to determine which groups differ

What kinds of activities do you engage in when using a device while viewing video content on a TV screen? An IAB and MARU Matchbox study captured multitasking activities of adults who use different devices while watching TV. The study reported that 320 of 444 (72%) smartphone users sampled, 194 of 347 (56%) of computer users sampled, and 141 of 261 (54%) of tablet users sampled used their device to check social media unrelated to the video while watching TV.

a. Is there evidence of a significant difference among the smartphone, computer, and tablet users with respect to the proportion who use their device to check social media unrelated to the video while watching TV? (Use $\alpha$ = 0.05).

b. Determine the p-value and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha$ = 0.05 to determine which groups differ.

Repeat (a) and (b) of the earlier exercise, assuming that only 10 social media users for each age group were surveyed. Discuss the implications of sample size on the $\chi^2$ test for differences among more than two populations.

Repeat (a) and (b) of previous Problem, assuming that only 100 individuals from each business group were surveyed. Discuss the implications of sample size on the $x^2$ test for differences among more than two populations.

Social media users use a variety of devices to access social networking; mobile phones are increasingly popular. However, is there a difference in the various age groups in the proportion of social media users who use their mobile phone to access social networking? A study showed the following results for the different age groups:

$$\begin{array}{c} \begin{array}{c} \hspace{140pt}\underline{\textbf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Age\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }} \end{array} \\ \begin{array}{lcc} \textbf{Use mobile phone to access}\\ \textbf{Social networking} & \bf18-34 & \bf 35 - 64 & \bf 65+\\ \hline \text{Yes} & 59\% & 36\% & 13\%\\ \text{No} & 41\% & 64\% & 87\% \end{array} \end{array}$$

Assume that 200 social media users for each age group were surveyed.

a. At the 0.05 level of significance, is there evidence of a difference among the age groups with respect to use of mobile phone for accessing social networking?

b. Determine the p-value in (a) and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha = 0.05$ to determine which age groups differ with respect to use of a mobile phone for accessing social networking.

d. Discuss the implications of (a) and (c). How can marketers use this information to improve their sales return on investment (ROI)?

An Employee Value Proposition (EVP) is about defining the essence of a company. The EVP is the value an employee receives from the employer; it defines the commitment the company will make to develop the employee in exchange for the effort the employee puts in to benefit the company. But do all agree on what makes a unique and compelling EVP? A study showed that 14% of business executives, 38% of HR leaders, and 33% of employees say that compensation (pay and rewards) makes for a unique and compelling EVP.

Assume that 200 individuals within each business group were surveyed.

a. Is there evidence of a difference among business groups with respect to the proportion that say compensation (pay and rewards) makes for a unique and compelling EVP?

b. Determine the p-value in (a) and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha$ = 0.05 to determine which business groups differ in the proportion that say compensation (pay and rewards) makes for a unique and compelling EVP.

What are travelers’ technologies of choice? Tablets account for a growing share of the multiuse devices travelers are using. An observational study of passengers on air, bus, and train travel found that 8.4% of airline passengers, 5.9% of Amtrak passengers, 4.9% of commuter train passengers, and 3.7% of curbside bus passengers were observed using a tablet at some point during their travel. Suppose these results were based on 500 passengers in each of the four transportation modes: airline, Amtrak train, commuter train, and curbside bus.

a. At the 0.05 level of significance, is there evidence of a difference among the transportation modes with respect to use of tablets?

b. Compute the p-value and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha = 0.05$ to determine which transportation modes differ.

Business sensor technology provides a way for companies to learn about their customers, employees, and operations; data captured from sensors can be used to improve engagement, sales, productivity, safety, and much more. A PwC survey of global business and IT executives found that 25% of automotive executives; 27% of energy, utilities, and mining executives; 30% of hospitality and leisure executives; 33% of industrial products executives; and 52% of retail and consumer executives say their companies are currently investing in business sensor technology.

Suppose these results were based on 500 business and IT executives in each of the five industries: Automotive; Energy, Utilities, and Mining; Hospitality and Leisure; Industrial Products; and Retail and Consumer.

a. At the 0.05 level of significance, is there evidence of a difference among the industries with respect to the proportion of executives that say their companies are currently investing in business sensor technology?

b. Compute the p-value and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha$ = 0.05 to determine which companies differ in their current investing in business sensor technology.

Do workers prefer to buy lunch rather than pack their own lunch? A survey of employed Americans found that 75% of the 18- to 24-year-olds, 77% of the 25- to 34-year-olds, 72% of the 35- to 44-year-olds, 58% of the 45- to 54-year-olds, 57% of the 54- to 64-year-olds, and 55% of the 65+ -year-olds buy lunch throughout the work week. Suppose the survey was based on 200 employed Americans in each of six age groups: 18 to 24, 25 to 34, 35 to 44, 45 to 54, 55 to 64, and 65+.

a. At the 0.05 level of significance, is there evidence of a difference among the age groups in the preference for buying lunch?

b. Determine the p-value in (a) and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha = 0.05$ to determine which age groups differ.

How common are financial cost or contractual constraints associated with smartphone ownership? A survey of smartphone owners found that 48% of the 18- to 29-year-olds, 38% of the 30- to 49-year-olds, 25% of the 50- to 64-year-olds, and 19% of those age 65 or older have reached the maximum amount of data they are allowed to use as part of their plan, at least on occasion.

Suppose the survey was based on 200 smartphone owners in each of the four age groups: 18 to 29, 30 to 49, 50 to 64, and 65+.

a. At the 0.05 level of significance, is there evidence of a difference among the age groups in the proportion of smartphone owners who have reached the maximum amount of data they are allowed to use as part of their plan, at least on occasion?

b. Determine the p-value in (a) and interpret its meaning.

c. If appropriate, use the Marascuilo procedure and $\alpha$ = 0.05 to determine which age groups differ.

Use the following contingency table:

$$\begin{array}{lcccc} & A & B & C & Total \\ \hline \$\mathbf{1} & 20 & 30 & 25 & 75 \\ \mathbf{2} & 30 & 20 & 25 & 75 \\ \hline Total & 50 & 50 & 50 & 150 \end{array}$$

a. Compute the expected frequency for each cell.

b. Compute $\chi_{S T A T}^2$. Is it significant at $\alpha=0.05$ ?

Use the following contingency table:

$$\begin{array}{llllc} & A & \mathbf{B} & \mathbf{C} & Total \\ \hline \mathbf{1} & 10 & 30 & 50 & 90 \\ \mathbf{2} & \frac{40}{50} & \frac{45}{75} & \frac{50}{100} & \frac{135}{225} \end{array}$$

a. Compute the expected frequency for each cell.

b. Compute $\chi_{\text {STAT }}^2$. Is it significant at $\alpha=0.05$ ?