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
(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 find: Thesample mean, sample standard deviation and the coefficient of variation for the lengths and widths.
Answer to Problem 1DHGP
Solution:
Variable | Mean | Standard deviation | Coefficient of variation |
length_(mm) | 438.4 | 96.4 | 21.98 |
width_(mm) | 383.6 | 89.4 | 23.3 |
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.
The result is obtained below:
Variable | Mean | Standard deviation | Coefficient of variation |
length_(mm) | 438.4 | 96.4 | 21.98 |
width_(mm) | 383.6 | 89.4 | 23.3 |
(b)
To find: The95% confidence interval for the population mean length of all Garrison Bay little neck clams.
Answer to Problem 1DHGP
Solution:
The95% confidence interval for the population mean length of all Garrison Bay little neck clams is between 406.5 and 470.3.
Explanation of Solution
Calculation:
Let x represents the lengths of little neck clams,
We have to find 95% confidence interval for
95% confidence interval is
The 95% confidence interval for
(c)
To find: The number of more little neck clams would be needed in a sample.
Answer to Problem 1DHGP
Solution:
The additional little neck clams needed is357.
Explanation of Solution
Calculation:
We have,
We have to find the sample size n,
The sample size needed to be 95% sure that the sample mean is within a maximal margin of error of 10 mm of the population mean length is 357.
So, the additional little neck clams needed
(d)
To find: The95% confidence interval for the population mean width of all Garrison Bay little neck clams.
Answer to Problem 1DHGP
Solution:
The95% confidence interval for the population mean width of all Garrison Bay little neck clams is between 354.03 and 413.23.
Explanation of Solution
Calculation:
Let y represents the widths of little neck clams,
We have to find 95% confidence interval for
95% confidence interval is
The 95% confidence interval for
(e)
To find: The number of more little neck clams would be needed in a sample.
Answer to Problem 1DHGP
Solution:
The additional little neck clams needed is 272.
Explanation of Solution
Calculation:
We have,
We have to find the sample size n,
The sample size needed to be 95% sure that the sample mean is within a maximal margin of error of 10 mm of the population mean length is 307.
So, the additional little neck clams needed
(f)
To explain: Whether the sample measurements length and width are independent or dependent.
Answer to Problem 1DHGP
Solution: The sample measurements length and width are dependent.
Explanation of Solution
The same 35 clams were used for measures of length and width. The sample measurements length and width are dependent because as the 95% confidence interval for length increases at same level of confidence, the width is decreased.
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Chapter 8 Solutions
Understanding Basic Statistics
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