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Answer: Lobster trap placement. Refer to the Bulletin of

ISBN: 9780321826237 51

Solution for problem 52E Chapter 7

Statistics for Business and Economics | 12th Edition

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Problem 52E

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. Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are reproduced in the accompanying table (and saved in the TRAPSPACE file). Let μ represent the average of the trap spacing measurements for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. In Exercise 5.35 you computed the mean and standard deviation of the sample measurements to be  meters and s = 11.6 meters, respectively. Suppose you want to determine if the true value of μ differs from 95 meters.

 93 99 105 94 82 70 86

From 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. Reprinted with permission from the University of Miami – Bulletin of Marine Science.

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

b. Since  is less than 95, a fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?

c. Compute the value of the test statistic.

d. Find the approximate p -value of the test.

e. Select a value of a , the probability of a Type I error. Interpret this value in the words of the problem.

f. Give the appropriate conclusion, based on the results of parts d and e.

g. What conditions must be satisfied for the test results to be valid?

h. In Exercise 5.35 you found a 95% confidence interval for μ . Does the interval support your conclusion in part f ?

Lobster trap placement. 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 in the accompanying table (and saved in the TRAPSPACE file). 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

From 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. Reprinted with permission from the University of Miami – Bulletin of Marine Science.

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?

Conclusions and Consequences for a Test of Hypothesis

 True State of Nature Conclusion H0 True Ha True Accept H0 (Assume H0 True) Reject H0 (Assume Ha True) Correct decision Type I error (probability α) Type II error (probability β) Correct decision
Step-by-Step Solution:

Step 1 of 9:

Trap spacing measurements  for a sample of seven teams of red spiny is

 93 99 105 94 82 70 86

The mean is 89.9 and the standard deviation is 11.6.

If we want to determine the true value of  differing from 95 meters.

Step 2 of 9:

The claim is to state the null and alternative hypothesis

the true value of differing from 95 meters.

Therefore, the null and alternative hypothesis are

against

Step 3 of 9:

b)  since = 89.9 is less than 95, a fisherman wants to reject the null hypothesis.

The claim is to suggest the problem with using such a decision rule.

The value of  varies from sample to sample. The next sample may vary that  is greater than 95.

Then, we must determine how unusual a value of  =89.9 is if the true mean is 95.

Step 4 of 9:

c)

The claim is to compute the value of test statistics

The test statistic t =

Where, =89.9, = 95, s = 11.6, and n = 7

=

=

= -1.1632

Hence, the test statistic t = -1.1632.

Step 5 of 9:

d)

The claim is to find the p-value of the test

From Minitab

> enter the data

> go to start - Basic statistics

> 12 -sample t-test

Hence, the p-value is 0.286.

Step 6 of 9

Step 7 of 9

ISBN: 9780321826237

Since the solution to 52E from 7 chapter was answered, more than 1944 students have viewed the full step-by-step answer. The answer to “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. Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are reproduced in the accompanying table (and saved in the TRAPSPACE file). Let ? represent the average of the trap spacing measurements for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. In Exercise 5.35 you computed the mean and standard deviation of the sample measurements to be meters and s = 11.6 meters, respectively. Suppose you want to determine if the true value of ? differs from 95 meters.939910594827086From 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. Reprinted with permission from the University of Miami – Bulletin of Marine Science.a. Specify the null and alternative hypothesis for this test.________________b. Since is less than 95, a fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?________________c. Compute the value of the test statistic.________________d. Find the approximate p -value of the test.________________e. Select a value of a , the probability of a Type I error. Interpret this value in the words of the problem.________________f. Give the appropriate conclusion, based on the results of parts d and e.________________g. What conditions must be satisfied for the test results to be valid?________________h. In Exercise 5.35 you found a 95% confidence interval for ? . Does the interval support your conclusion in part f ?Lobster trap placement. 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 in the accompanying table (and saved in the TRAPSPACE file). Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico.939910594827086From 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. Reprinted with permission from the University of Miami – Bulletin of Marine Science.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?Conclusions and Consequences for a Test of Hypothesis True State of NatureConclusionH0 TrueHa TrueAccept H0 (Assume H0 True) Reject H0 (Assume Ha True)Correct decisionType I error (probability ?)Type II error (probability ?) Correct decision” is broken down into a number of easy to follow steps, and 539 words. This full solution covers the following key subjects: lobster, TRAP, true, bulletin, spiny. This expansive textbook survival guide covers 15 chapters, and 1630 solutions. The full step-by-step solution to problem: 52E from chapter: 7 was answered by , our top Business solution expert on 07/21/17, 05:42AM. Statistics for Business and Economics was written by and is associated to the ISBN: 9780321826237. This textbook survival guide was created for the textbook: Statistics for Business and Economics , edition: 12.

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