Strategic placement of lobster traps is one of the keys for

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

a. Identify the target parameter for this study.

b. Compute a point estimate of the target parameter.

c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?

d. Find a 95% confidence interval for the target parameter.

e. Give a practical interpretation of the interval, part d, that is, what does the confidence interval mean or tell us?

f. What conditions must be satisfied for the interval, part d, to be valid?

g. How many teams of fishermen would need to be sampled in order to reduce the width of the confidence interval to 5 meters? Note that the width of the interval is equal to two times the margin of error (2E).

Solution

a)

(µ)

b)

Point estimate = ( 93+99+105+94+82+70+86)/7 = 89.86

c)

Central limit theorem does not apply since we don\'t have a large sample.

d)

Margin of error = 1.96 * 11.6251 / sqrt(7) = 8.6

95% CI = ( 89.86 - 8.6 , 89.86 + 8.6)

= ( 81.26, 98.46)

e)

We are 95% confident that the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico is between 81.26 meters and 98.46 meters

f)

• A random sample is selected from the target population

• The population has a relative frequency distribution that is approximately normal.