Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of
how engineers design social robots, Exercise 2.7 (p. 38). Recall that a social (or service) robot is designed to entertain, educate, and care for human users. 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 engineer's claim.
c. Assuming the claim is true, determine the number of social robots in the sample 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 α = .05.