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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,*

(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?

**(a)**

To determine

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

**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*, *y*by 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.

Understanding Basic Statistics

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