Question

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 6.29 (p. 348). Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are reproduced in the accompanying table. Let \(\mu \) represent the average of the trap-spacing measurements for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. In Exercise 6.29 you computed the mean and standard deviation of the sample measurements to be \(\bar x = 89.9\) meters and s = 11.6 meters, respectively. Suppose you want to determine if the true value of \(\mu \) differs from 95 meters

a. Specify the null and alternative hypotheses for this test.

Short answer

a)

\(\begin{array}{}{H_0}:\mu = 95\\{H_a}:\mu \ne 95\end{array}\)

Step-by-step solution

Given Information

The sample size is 7.

The mean and standard deviation is given. i.e.

\(\bar x = 89.9\,and\,s = 11.6\)

Standard deviation

The standard deviation is a metric that calculates as the sum of squares of the variance as well as quantifies the dispersion of a data compared to its mean. The standard deviation is determined as the sum of squares of the variance by calculating the departure of each piece of data from the mean.In descriptive statistics, the standard deviation is the amount of dispersal as well as scattering of sample points compared to their mean.

Step 3:

The hypothesis is given by

\(\begin{array}{}{H_0}:\mu = 95\\{H_a}:\mu \ne 95\end{array}\)