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Garrison Bay is a small hay in Washington stale. A popular recreational activity in the bay is clam digging. Forseveral years, this harvest has been monitored and the size distribution of clams recorded. Data for lengths and widths of little neck clams (Protothacastaminea) were recorded by a method of systematic sampling in a study done by S. Scherba and V. F. Gallucci ("The Application of Systematic Sampling to a Study of Infaunal Variation in a Soft Substrate Intertidal Environment." Fishery Bulletin, Vol. 74, pp 937-948). The data in Tables 8-4 and 8-5 are the lengths and widths for 35 little neck clams. (a) Use a calculator to compute the sample mean and sample standard deviation for the lengths and widths Compute the coefficient of variation for each. (b) Compute a 95% confidence interval for the population mean length of all Garrison Bay little neck clams. (c) How many more little neck clams would be needed in a sample if you wanted to be 95% sure that the sample mean length is within a maximal margin of error of 10 mm of the population mean length? TABLE 8-4 Lengths of Little Neck Clams (mm) 530 517 505 512 487 481 485 479 452 468 459 449 472 471 455 394 475 335 508 486 474 465 420 402 410 393 389 330 305 169 91 537 519 509 511 TABLE 8-5 Widths of Little Neck Clams (mm) 494 477 471 413 407 427 408 430 395 417 394 397 402 401 385 338 422 288 464 436 414 402 383 340 349 333 356 268 264 141 11 498 456 433 447 (d) Compute a 95% confidence interval for the population mean width of all Garrison Bay little neck clams. (c) How many more little neck claim would he needed in a sample if you wanted to be 95% sure that the sample mean width is within a maximal margin of error of 10 mm of the population mean width? (0 The same 35 clams mere used for measures of length and width. Are the sample measurements length and width independent or dependent? Why?

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Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075

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Chapter
Section
BuyFindarrow_forward

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075
Chapter 8, Problem 1DHGP
Textbook Problem
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Garrison Bay is a small hay in Washington stale. A popular recreational activity in the bay is clam digging. Forseveral years, this harvest has been monitored and the size distribution of clams recorded. Data for lengths and widths of little neck clams (Protothacastaminea) were recorded by a method of systematic sampling in a study done by S. Scherba and V. F. Gallucci ("The Application of Systematic Sampling to a Study of Infaunal Variation in a Soft Substrate Intertidal Environment." Fishery Bulletin, Vol. 74, pp 937-948). The data in Tables 8-4 and 8-5 are the lengths and widths for 35 little neck clams.

(a) Use a calculator to compute the sample mean and sample standard deviation for the lengths and widths Compute the coefficient of variation for each.

(b) Compute a 95% confidence interval for the population mean length of all Garrison Bay little neck clams.

(c) How many more little neck clams would be needed in a sample if you wanted to be 95% sure that the sample mean length is within a maximal margin of error of 10 mm of the population mean length?

TABLE 8-4 Lengths of Little Neck Clams (mm)

530 517 505 512 487 481 485 479 452 468
459 449 472 471 455 394 475 335 508 486
474 465 420 402 410 393 389 330 305 169
91 537 519 509 511

TABLE 8-5 Widths of Little Neck Clams (mm)

494 477 471 413 407 427 408 430 395 417
394 397 402 401 385 338 422 288 464 436
414 402 383 340 349 333 356 268 264 141
11 498 456 433 447

(d) Compute a 95% confidence interval for the population mean width of all Garrison Bay little neck clams.

(c) How many more little neck claim would he needed in a sample if you wanted to be 95% sure that the sample mean width is within a maximal margin of error of 10 mm of the population mean width?

(0 Thesame 35 clams mere used for measures of length and width. Are the sample measurements length and width independent or dependent? Why?

(a)

To determine

To find: Thesample mean, sample standard deviation and the coefficient of variation for the lengths and widths.

Explanation of Solution

Calculation:

Let x represents the lengths of little neck clams and y represent the widths of little neck clams.

To find sample mean, sample standard deviation and the coefficient of variationfor x, yby using Minitab, follow the instructions:

Step 1: Enter the data in Minitab Software.

Step 2: Go to Stat > Basic statistics > Display Descriptive Statistics

Step 3: Select x, y in variable.

Step 4: Go to ‘statistics’ choose Mean, Standard deviation, Coefficient of variation...

(b)

To determine

To find: The95% confidence interval for the population mean length of all Garrison Bay little neck clams.

(c)

To determine

To find: The number of more little neck clams would be needed in a sample.

(d)

To determine

To find: The95% confidence interval for the population mean width of all Garrison Bay little neck clams.

(e)

To determine

To find: The number of more little neck clams would be needed in a sample.

(f)

To determine

To explain: Whether the sample measurements length and width are independent or dependent.

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Chapter 8 Solutions

Understanding Basic Statistics
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