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Chapter 6: Q69E (page 363)

Lobster trap placement. Refer to the Bulletin of MarineScience(April 2010) study of lobster trap placement,Exercise 6.29 (p. 348). Recall that you used a 95% confidenceinterval to estimate the mean trap spacing (in meters)for the population of red spiny lobster fishermen fishing inBaja California Sur, Mexico. How many teams of fishermenwould need to be sampled in order to reduce the width ofthe confidence interval to 5 meters? Use the sample standarddeviation from Exercise 6.29 in your calculation.

Short Answer

Expert verified

The 84 teams of fishermen would need to be sampled in order to reduce the width ofthe confidence interval to 5 meters.

Step by step solution

01

Given information

Referring to Exercise 6.29 (p. 348)

02

Finding the sample standard deviation

No

x


1

93

9.877551

2

99

83.59184

3

105

229.3061

4

94

17.16327

5

82

61.73469

6

70

394.3061

7

86

14.87755

Sum

629

810.8571

Here the values are given

∑i=17xi=629   and   ∑i=17(xi−x¯)2=810.8571

The sample mean is

role="math" localid="1658296119475" x¯=∑i=17xi7=6297=89.85714

The sample standard deviation is

s=∑i=17(xi−x¯)27−1=810.85716=11.6251

03

Finding the sample size

Here the width of the confidence interval is 5

i.e,2SE=5SE=2.5

Here the standard error is 2.5

The value of the standard deviation is 11.6251

The critical value for a 95% confidence interval iszα/2=z0.05/2=z0.025=1.96

SE=zα/2snn=z2α/2s2SE2n=1.962×11.625122.52n=83.06643n≃84

The required sample size is 84.

Hence 84 teams of fishermen would need to be sampled in order to reduce the width ofthe confidence interval to 5 meters.

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Most popular questions from this chapter

Monitoring phone calls to a toll-free number. A largefood-products company receives about 100,000 phone callsa year from consumers on its toll-free number. A computermonitors and records how many rings it takes for an operatorto answer, how much time each caller spends “on hold,” andother data. However, the reliability of the monitoring systemhas been called into question by the operators and their labour unions. As a check on the computer system, approximatelyhow many calls should be manually monitored during thenext year to estimate the true mean time that callers spend onhold to within 3 seconds with 95% confidence? Answer thisquestion for the following values of the standard deviation ofwaiting times (in seconds): 10, 20, and 30.

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What is the confidence level of each of the following confidence intervals μ?

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