# solution

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of how engineers design social robots, Exercise 2.5 (p. 72). In a random sample of 106 social robots obtained through a Web search, the researchers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Prior to obtaining these sample results, a robot design engineer stated that 50% of all social robots produced have legs only, 30% have wheels only, 10% have both legs and wheels, and 10% have neither legs nor wheels.

a. Explain why the data collected for each sampled social robot are categorical in nature.

b. Specify the null and alternative hypotheses for testing the design engineerâ€™s claim.

c. Assuming the claim is true, determine the number of social robots in the sample that you expect to fall into each design category.

d. Use the results to compute the chi-square test statistic.

e. Make the appropriate conclusion using a = .05.

Exercise 2.5

Do social robots walk or roll? A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.

a. What type of graph is used to describe the data?
b. Identify the variable measured for each of the 106 robot designs.
c. Use the graph to identify the social robot design that is currently used the most.
d. Compute class relative frequencies for the different categories shown in the graph.
e. Use the results from part d to construct a Pareto diagram for the data.

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