In order to ensure the public's health and safety, state health inspectors are required to rate the cleanliness and quality of all restaurants in the state. Restaurants that consistently score below a certain level often lose their licenses to operate. From a sample of 10 restaurants, two health inspectors give the ratings shown in the accompanying table, where a score of 10 denotes excellence in cleanliness and quality. The data are also on the text website, labeled Inspectors.

Restaurant Inspector A's Rating Inspector B's Rating 1 9 8 2 5 6 3 10 8 4 5 4 5 2 3 6 7 5 7 8 6 8 4 1 9 3 2 10 8 9

a. Using the sign test, specify the com peting hypotheses to determ ine w hether the ratings are significantly different between the tw o health inspectors.

b. Calculate the value o f the test statistic.

c. Calculate the p -value.

d. At the 5% significance level, do the data suggest that the ratings significantly differ?