7.125 Number of critical food violations. The results of a major city’s restaurant inspections are available through its online newspaper.45 Critical food violations are those that put patrons at risk of getting sick and must immediately be corrected by the restaurant. An SRS of n = 200 inspections from the more than 16,000 inspections since January 2012 were collected, resulting in violations and s = 1.822 violations.

  1. (a) Test the hypothesis that the average number of critical violations is less than 1.5 using a significance level of 0.05. State the two hypotheses, the test statistic, and P-value.

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

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

  4. (d) These data are integers ranging from 0 to 10. The data are also skewed to the right, with 79% of the values either a 0 or a 1. Given this information, do you think use of the t procedures is appropriate? Explain your answer.