Length of stay. According to the data reported by the Tourism Bureau, Ministry of Transportation and Communications in CEIC, the average length of stay in Taiwan from January 2008 to February 2021 was 12 nights. A random sample of 35 of the current lengths of stay is collected. This data (in number of nights) is shown in the following table. 8 2 12 15 11 10 18 9 12 11 9 11 13 7 7 12 19 18 7 18 20 4 1 7 5 2 6 20 13 2 4 2 14 16 15

a. What are the appropriate null and alternative hypotheses to test whether the average length of stay in Taiwan is less than 12 nights?

b. Conduct the test at a = .05. Does the sample data provide sufficient evidence to conclude that the average length of stays in Taiwan is less than 12 nights?

c. In conducting the test, was it necessary to assume that the population of average full-service fees was normally distributed? Justify your answer.