Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. An observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, was conducted and the results published in Bulletin of Marine Science (April 2010). One of the variables of interest was the average distance separating traps—called trap spacing—deployed by the same team of fishermen. Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are shown below. (Source: Based on Shester, G. G. “Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions,” Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1), pp. 479–498.) Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico.
93 99 105 94 82 70 86
Previously you calculated the mean and standard deviation of the seven sample measurements to be x ̅ = 89.9 meters and s = 11.6 meters, respectively. Now the researchers want to know whetherσ^2, the variation in the population of trap-spacing measurements, is larger than 10 m2. They will conduct a test of hypothesis using α = 0.05.
a.) Note that s2 > 10. Consequently, a fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?
b.) Compute the value of the test statistic.
c.) Find the approximate p-value of the test
d.) Give the appropriate conclusion.
e.) What conditions must be satisfied for the test results to be valid?