A social (or service) robot is designed to entertain, educate, and care for huma

Question

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 that you expect to fall into each design category; that is, find the expected number for each category.

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

e. Make the appropriate conclusion using = .05.

Explanation / Answer

H0: Social robots produced are in proportion 50%, 30%, 10% and 10%

Ha: They are not in the above proporiton

Two tailed chi square test

Prepare contingency table

Chi square = 8.730 with df = 3

p value = 0.0331

As p < 0.05, reject H0

The robots are not in the proportion claimed.

With legs Wheels Legs&wheels no legs,no wheels Total Observed 63 20 8 15 106 Expected 53 31.8 10.6 10.6 106 (O-e)^2 100 139.24 6.76 19.36 Chi squ 1.886792 4.378616 0.637736 1.826415094 8.72956

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