Number of critical food violations. The results of a major city's restaurant inspections are available through its online newspaper.31 Critical food violations are those that put patrons at risk of getting sick and must be corrected immediately by the restaurant. An SRS of n = 200 inspections from the more than 14,000 inspections since January 2009 was collected in which x = 0.65 critical violations and s = 0.88 critical violations.

(a) Test the hypothesis that the average number of critical violations is less than 0.75 using a significance level of 0.05. State the two hypotheses, the test statistic, and P-value.

(b) Construct a 95% confidence interval for the average number of critical violations and summarize your result.

(c) Which of the two summaries (significance test versus confidence interval) do you find more helpful in this case? Explain your answer.

(d) These data are integers ranging from 0 to 9. The data are also skewed to the right, with 70% of the values either a 0 or a 1. Given this information, do you feel that use of the t procedures is appropriate? Explain your answer.