Lobster trap placement. An observational study of teams fishing for the red spin

Question

Lobster trap placement. 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 (Apr. 2010). One of the variables of interest was the average distance separating traps-called trap spacing-deployed by the same team fishermen. Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are shown in the accompanying table. Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. 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, Apr.2010 (Table 1), pp. 479-498. 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. f. What conditions must be satisfied for the interval, part d, to be valid?

Explanation / Answer

(a) population mean, is target parameter

(b) its point estimate=sample mean=sum/n=629/7=89.86

(c) since sample size is small(less than 30), so we should not use z-statistic

(d) (1-alpha)*100% confidence interval for population mean=mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=89.86±t(0.05/2, 7-1)*11.63/sqrt(7)=89.86±2.45*11.63/sqrt(7)

=89.86±10.77=(79.09,100.63)

(e)To interpret a confidence interval remember that the sample information is random - but there is a pattern to its behavior if we look at all possible samples. Each possible sample gives us a different sample proportion and a different interval. But, even though the results vary from sample-to-sample, we are "confident" because the margin-of-error would be satisfied for 95% of all samples

(f) sample should come from normal distribution/population

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