As of $2018,$ there were more than $9,000$ Dunkin' Donuts stores worldwide, including more than $6,400$

franchised restaurants in the United States and $2,600$ international shops in $31$ countries. The company clocked

worldwide sales of $$5\mathrm{.}7$ billion during the fiscal year $2017.$ This impressive growth would not have been possible

without extensive marketing research and a commitment to quality. Bill Rosenberg began the culture within the

company of listening to what the customer wanted and then providing it$,$ and that tradition continues today.

Marketing research in the form of focus groups and survey research revealed that customers select a coffee and

donut shop based on five factors: accessibility, quality, variety, image, and affordability. Assume that the

company has just decided to conduct another research to analyze the perceived image of Dunkin Donuts and its

major competitors in terms of these five factors in the light of coffee shop visiting behavior and consumers'

preferences. Two of the several research questions are as follows;

Are female consumers differ from male consumers in terms of each of the perceived qualities of Dunkin

Donuts?

Is there any difference between Dunkin Donuts and Starbucks as the primary competitor of the company in

terms of each of the image dimensions $($accessibility$,$ quality, variety, image, and affordability$)$

a$)$ The perceived image dimensions are measured by semantic differential scale in the questionnaire. Please

design a semantic differentiate scale that can be used in a nationwide study to measure the perceived image of

Dunkin Donuts and Starbucks.

b$)$ Please state the related hypotheses

c$)$ Suggest the most appropriate test statistics for each situation and discuss all the factors influencing the choice

of data analysis method.