Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise. Recall that the variable of interest was the average distance separating traps—called trap spacing—deployed by teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico. The trap spacing measurements (in meters) for a sample of 7 teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap spacing measurements for 8 teams from the Punta Abreojos (PA) fishing cooperative are listed. (All these data are saved in the TRAPSPACE file). For this problem, we are interested in comparing the mean trap spacing measurements of the two fishing cooperatives.

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 ), 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 90% confidence interval for the target parameter.

e. Use the interval, part d, to make a statement about the difference in mean trap spacing measurements of the two fishing cooperatives.

f. What conditions must be satisfied for the inference, part e, to be valid?

Solution:

Step 1 of 4:

The trap spacing measurements for a sample of 7 teams from the Bahia Tortugas (BT) fishing cooperative are given in the table.

BT cooperative |
93 |
99 |
105 |
94 |
82 |
70 |
86 |

PA cooperative |
118 |
94 |
106 |
72 |
90 |
66 |
153 |
98 |

The trap spacing measurements for 8 teams from the Punta Abreojos (PA) fishing cooperative are listed.

We have to compare the mean trap spacing measurements of two fishing cooperatives.

We have to,

(a) Identify the target parameter for this study.

(b)Compute a point estimate of the target parameter.

(c) Find what is the problem with using the normal(Z) statistic to find a confidence interval for the target parameter.

(d) Find a 90% confidence interval for the target parameter.

(e) make a statement about the difference in mean trap spacing measurements of the two fishing

Cooperatives.

(f) Find the conditions must be satisfied for the inference in part to be valid.

Step 3 of 4:

(a)

The target parameter is, difference in mean trap measurements between the Bahia Tortugas fishing cooperative and the Punta Abreojos fishing cooperative.

(b)

By using the minitab we will get the descriptive statistics for Bahia Tortugas fishing cooperative and the Punta Abreojos fishing cooperative as:

From the descriptive statistics, the point estimate of the target parameter ,

- = 89.86-99.63

= - 9.77

Therefore the point estimate of the target parameter, is -9.77.

(c)

Since the sample sizes for both samples are so small( n<30), the Central Limit Theorem does not apply.

In addition, here the population standard deviation are unknown so we have to use sample standard deviation.

Since the both conditions are necessary to use a Z- statistic for testing, we cannot use Z-statistic to find a confidence interval for the target parameter.

Step 3 of 4:

(d)

We have to find the 90% confidence interval for ().

The 100(1-)% confidence interval for () is,

( ( - ) ).

=

=

=

= 466.0569

For the confidence coefficient, 0.90.

= 0.05

Here df=

= 7+8-2

= 13

From the t-distribution table with degrees of freedom 13,

= 1.771

90% CI for ().

( 89.86-99.631.771)

( -9.7719.787)

( -29.557, 10.017)