The results of a major city's restaurant inspections are available through its online newspaper. Critical food violations are those that put patrons at risk of getting sick and must be immediately corrected by the restaurant. An SRS of n = 200 inspections from the more than 4400 inspections since January 2008 had x‾ = 1.20 violations and s = 1.81 violations.
a) Test the hypothesis, using α= 0.05, that the average number of critical violations is less than 1.5. 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 0-9. The data are also skewed to the right, with 70% of the values either a 0 or 1. Given this information, do you feel use of the t procedures is appropriate? Explain your answer.