Solutions for the exercises in Chapter 8.
| Exercise | Group | No. | Question | Answer |
| 8.1 | I | 1-a) | The sample size | 31 |
| The range of the sample values | 469 cm | |||
| The median | 267 cm | |||
| The mean | 261.9 cm | |||
| The total value | 8118 cm | |||
| The sample variance | 15636.5 | |||
| The sample standard deviation. | 125.0 cm | |||
| The sample coefficient of variation. | 0.48 | |||
| 8.1 | II | 1 | From this data calculate the mean and the variance. | Mean(x) = 23.2 cm Var(x) = 12.5 |
| 2 | Choose an adequate class interval and build up a table with the length frequencies distribution | Class interval chosen -1 cm Because it is simple, and gives an adequate number of classes (between 15 and 30) | ||
| 3-a) | The sample mean and sample variance. Compare this results with the ones obtained in 1 | Sample mean = 23.2 cm Sample variance = 12.5 The values of the statistics are equal. Since the class interval used was the same as the resolution of the original measurements, no information was lost. | ||
| 3-b) | Three statistics of location | Mean = 23.2 cm Median = 22.5 cm Mode = 20 cm | ||
| 3-c) | Three statistics of dispersion | Inter Quartile Range = 5.5 cm Variance = 12.49 CV = 0.15 | ||
| 3-d) | Number of individuals with a length less than 20 cm | 41 | ||
| 3-e) | Percentage of individuals with a length equal to or greater than 20 cm | 79% | ||
| 3-f) | Percentage of observations between 23 and 25 cm | 15% | ||
| 3-g) | The value that corresponds to a length equal to or greater than 45% of all the observations | 21.5 cm | ||
| 3-h) | The value that corresponds to a length less than 21% of all the observations | 26.5 cm | ||
| 3-i) | The quantile of order 96% | 30.5 cm | ||
| 8.2 | I | 1-a) | Relative frequencies of number of boats by fishing gear | Purse-seines: 0.3 Trawls: 0.21 Handlines: 0.17 Longlines: 0.23 Trammel nets: 0.09 Purse-seines: 0.3 |
| 1-b) | Percentage of vessels that operate handlines | 17% | ||
| 1-c) | Percentage of vessels that operate trammel nets | 9% | ||
| 2-a) | Relative frequency of boats not operating trammel nets | 0.91 | ||
| 2-b) | Percentage of boats operating purse seines or longlines | 53% | ||
| 2-c) | Relative frequency of boats that do not operate with handlines, nor trammel nets, nor longlines | 0.51 | ||
| 2-d) | Proportion of the total fleet that are small boats without engine | 0.25 | ||
| 2-e) | Proportion of the total fleet that are small boats with engine | 0.37 | ||
| 2-f) | Proportion of the total fleet that are small boats | 0.62 | ||
| 2-g) | Check that the proportion of 2.f) is the sum of 2.d) plus 2.e) | 0.62 = 0.25+0.37 | ||
| 3-a) | Proportion of the small boats without engine that operate handlines | 0.34 | ||
| 3-b) | Proportion of the total fleet that are small boats without engine | 0.25 | ||
| 3-c) | Proportion of the total fleet that are small boats without engine operating handlines | 0.08 | ||
| 3-d) | Check that the proportion of 3.c) is the product of 3.a) times 3.b) | 0.08 = 0.34×0.25 | ||
| 4-a) | Percentage of small boats without engine operating handlines or longlines | 65% | ||
| 4-b) | Percentage of purse seiners operating purse seines | 100% | ||
| 4-c) | Relative frequency of vessels that are not purse-seiners. | 81% | ||
| 4-d) | Percentage of small boats with engine that operate trawls | 4% | ||
| 4-e) | Percentage of the fleet that fishes with traps | 0% | ||
| 8.2 | II | 1-a) | Probability that the boat operates handlines | 0.17 |
| 1-b) | Probability that the boat operates Trammel nets | 0.09 | ||
| 1-c) | Probability that the boat does not operate trammel nets | 0.91 | ||
| 1-d) | Probability that the boat operates purse-seines or longlines. | 0.53 | ||
| 1-e) | Probability that the boat does not operate handlines, nor longlines nor trammel nets | 0.51 | ||
| 2-a) | Probability that the boat will be a small boat without engine | 0.245 | ||
| 2-b) | Probability that the boat will be a small boat with engine | 0.374 | ||
| 2-c) | Probability that the boat will be a small boat | 0.62 | ||
| 2-d) | Show that the probability 2.c) is equal to the sum of probability 2.a) plus the probability 2.b) | 0.619 = 0.245+0.374 | ||
| 3-a) | Probability of the boat being a purse seiner | 0.189 | ||
| 3-b) | Probability of the boat being a stern trawler | 0.192 | ||
| 3-c) | Probability of the boat not being a purse seiner nor a stern trawler | 0.619 | ||
| 3-d) | Show that probability 3.c) is equal to probability 2.c) | Shown from the comparison of the values | ||
| 4-a) | If we choose a boat from the small boats without engine, what is the probability that she operates with handline? | 0.338 | ||
| 4-b) | If we choose a boat out of the total fleet what is the probability that she is a small boat without engine? | 0.245 | ||
| 4-c) | If we choose a boat out of the total fleet what is the probability that she is a small boat without engine operating with handline? | 0.083 | ||
| 4-d) | Check that the probability of 4.c) is equal to the product of the probability of 4.a) times the probability of the 4.b). | 0.083 = 0.338×0.245 | ||
| 8.2 | III | 1-a) | Probability of X being less than or equal to 18 | 0.097 |
| 1-b) | Probability of X being greater than 18 | 0.903 | ||
| 1-c) | Probability of X being less than 25 | 0.986 | ||
| 1-d) | Probability of X being between 18 and 25 | 0.889 | ||
| 2-a) | x such that Prob {X ≤ x} = 0.8413 | 22.60 | ||
| 2-b) | x such that Prob {X ≥ x} = 0.9772 | 16.60 | ||
| 2-c) | x such that Prob {X < x} = 0.9986 | 26.58 | ||
| 2-d) | x such that x is the 95% quantile of the distribution of X | 23.89 | ||
| 2-e) | x such that x is the median of the distribution of X | 20.60 | ||
| 8.2 | IV | 1-a) | Probability of the values of Z being between -1 and 1 | 0.683 |
| 1-b) | Probability of the values of Z being between -2 and 2 | 0.954 | ||
| 1-c) | Probability of the values of Z being between -3 and 3 | 0.997 | ||
| 2-a) | The z1 value for which the probability that the values of the variable Z will be smaller than z1 is 2.5% (Prob{Z<z1} = 0.025) | -1.96 | ||
| 2-b) | The z2 value for which the probability of the variable Z being smaller than z2 is 97.5% (Prob{Z<z2} = 0.975) | 1.96 | ||
| 3-a) | Probability that the variable Z will be within the interval (z1, z2) given by (Prob{Z<z1} = 0.025) (Prob{Z<z2} = 0.975) | 0.950 | ||
| 3-b) | Probability that the variable Z will be within the interval (z1, z2) given by (Prob{Z<z1} = 0.004)Prob{Z<z2} = 0.954). | 0.950 | ||
| 3-c) | Probability that the variable Z will be within the interval (z1, z2) given by (Prob{Z<z1} = 0.012) (Prob{Z<z2} = 0.962) | 0.950 | ||
| Verify that the smallest of these intervals is the interval with symmetrical values, z1 and z2 | Width 3-a) = 1.96-(-1.96) = 3.92 Width 3-b) =1.68-(-2.65) = 4.33 Width 3-c) = 1.77-(-2.26) = 4.03 | |||
| 8.2 | V | 1-a) | Prob {t(10) >1.812} | 0.050 |
| 1-b) | Prob {t(19) <1.729} | 0.950 | ||
| 1-c) | Prob {-1.34 < t(15) < +2.602} | 0.890 | ||
| 2-a) | a such that Prob {t(8) < a} = 0.95 | 1.860 | ||
| 2-b) | a such that Prob {t(26) > a} = 0.99 | -2.479 | ||
| 2-c) | a such that Prob {-a < t(20) < +a} = 0.95 | 2.086 | ||
| 3-a) | a such that Prob {t < a} = 0.95, with 40, 60, 120 and infinite degrees of freedom | 40 df: a = 1.684 60 df: a = 1.671 120 df: a = 1.658 ∞ df: a = 1.645 | ||
| 3-b) | Compare a obtained in 3.a) with a such that Prob {Z < a} = 0.95 | a (Z) = 1.645 = a (t∞) |
| 8.2 | VI | 1 | Show that the expected value of the random variable X is equal to P | ![]() | ||||
| 2 | Show that the variance of the random variable X is equal to PQ | ![]() | ||||||
| 8.3 | I | 1-a) | Mean shrimp landing per sampled fishing trip | 698.7 Kg | ||||
| 1-b) | Variance of the sampled landings | 137 696 | ||||||
| 1-c) | Standard deviation of the sampled landings | 371.1 Kg | ||||||
| 2 | Estimate of the total amount of shrimp landed in that week | 6 986.7 Kg | ||||||
| 8.3 | II | 1-a) | Average shrimp landing per fishing trip during that week | 542 Kg | ||||
| 1-b) | Population variance and modified variance of the landings | σ2 = 127 730 S2 = 141 922 | ||||||
| 1-c) | Standard deviation of the landings | 357.4 Kg | ||||||
| 1-d) | Total amount of shrimp landed | 5 420 Kg | ||||||
| 1-e) | Proportion of all landings below 400 Kg | 0.300 | ||||||
| 1-f) | Relative frequency of landings between 400 and 800 Kg | 0.400 | ||||||
| 2 | Build at least 10 samples of 3 landings each that could have been selected from that population. | Sample no. | Land 1 | Land 2 | Land 3 | |||
| 1 | 538 | 0 | 906 | |||||
| 2 | 538 | 0 | 230 | |||||
| 3 | 538 | 0 | 598 | |||||
| 4 | 538 | 0 | 20 | |||||
| 5 | 538 | 0 | 435 | |||||
| 6 | 230 | 598 | 0 | |||||
| 7 | 230 | 598 | 435 | |||||
| 8 | 230 | 598 | 859 | |||||
| 9 | 230 | 598 | 1123 | |||||
| 10 | 230 | 598 | 711 | |||||
| 3 | Repeat the calculations done on number 1. a) to d), for each of these samples | Sample. no. | Average | Var | SD | Total | ||
| 1 | 481 | 207617 | 456 | 4813 | ||||
| 2 | 256 | 72868 | 270 | 2560 | ||||
| 3 | 379 | 108441 | 329 | 3787 | ||||
| 4 | 186 | 93028 | 305 | 1860 | ||||
| 5 | 324 | 81546 | 286 | 3243 | ||||
| 6 | 276 | 90988 | 302 | 2760 | ||||
| 7 | 421 | 34003 | 184 | 4210 | ||||
| 8 | 562 | 99864 | 316 | 5623 | ||||
| 9 | 650 | 201416 | 449 | 6503 | ||||
| 10 | 513 | 63259 | 252 | 5130 | ||||
| 4 | Compare the values of the statistics obtained in the previous item with the values of the corresponding population parameters. | The values of these statistics both over-estimate and under-estimate the corresponding population parameters | ||||||
| 8.3 | III | 1 | Histogram of the sampling distribution of the estimator, , using an appropriate class interval. | Appropriate Class Interval: 50 Kg (approx. 20 classes) | ||||
Sampling distribution - Mean landing

| 8.3 | III | 2-a) | The 120 values of the estimator | No. | Mean Land |
| 1 | 1481.3 | ||||
| 2 | 256.0 | ||||
| 3 | 378.7 | ||||
| 4 | 186.0 | ||||
| 5 | 324.3 | ||||
| 6 | 465.7 | ||||
| 7 | 553.7 | ||||
| 8 | 416.3 | ||||
| 9 | 558.0 | ||||
| 10 | 680.7 | ||||
| 11 | 488.0 | ||||
| 12 | 626.3 | ||||
| 13 | 767.7 | ||||
| 14 | 855.7 | ||||
| 15 | 718.3 | ||||
| 16 | 455.3 | ||||
| 17 | 262.7 | ||||
| 18 | 401.0 | ||||
| 19 | 542.3 | ||||
| 20 | 630.3 | ||||
| 21 | 493.0 | ||||
| 22 | 385.3 | ||||
| 23 | 523.7 | ||||
| 24 | 665.0 | ||||
| 25 | 753.0 | ||||
| 26 | 615.7 | ||||
| 27 | 331.0 | ||||
| 28 | 472.3 | ||||
| 29 | 560.3 | ||||
| 30 | 423.0 | ||||
| 31 | 610.7 | ||||
| 32 | 698.7 | ||||
| 33 | 561.3 | ||||
| 34 | 840.0 | ||||
| 35 | 702.7 | ||||
| 36 | 790.7 | ||||
| 37 | 378.7 | ||||
| 38 | 501.3 | ||||
| 39 | 308.7 | ||||
| 40 | 447.0 | ||||
| 41 | 588.3 | ||||
| 42 | 676.3 | ||||
| 43 | 539.0 | ||||
| 44 | 276.0 | ||||
| 45 | 83.3 | ||||
| 46 | 221.7 | ||||
| 47 | 363.0 | ||||
| 48 | 451.0 | ||||
| 49 | 313.7 | ||||
| 50 | 206.0 | ||||
| 51 | 344.3 | ||||
| 52 | 485.7 | ||||
| 53 | 573.7 | ||||
| 54 | 436.3 | ||||
| 55 | 151.7 | ||||
| 56 | 293.0 | ||||
| 57 | 381.0 | ||||
| 58 | 243.7 | ||||
| 59 | 431.3 | ||||
| 60 | 519.3 | ||||
| 61 | 382.0 | ||||
| 62 | 660.7 | ||||
| 63 | 523.3 | ||||
| 64 | 611.3 | ||||
| 65 | 578.0 | ||||
| 66 | 385.3 | ||||
| 67 | 523.7 | ||||
| 68 | 665.0 | ||||
| 69 | 753.0 | ||||
| 70 | 615.7 | ||||
| 71 | 508.0 | ||||
| 72 | 646.3 | ||||
| 73 | 787.7 | ||||
| 74 | 875.7 | ||||
| 75 | 738.3 | ||||
| 76 | 453.7 | ||||
| 77 | 595.0 | ||||
| 78 | 683.0 | ||||
| 79 | 545.7 | ||||
| 80 | 733.3 | ||||
| 8.3 | III | 2-b) | Expected value of the estimator | 542.0 Kg | |
| 2-c) | Sampling variance of the estimator | 33 115.2 | |||
| 2-d) | Error of the estimator | 182.0 Kg | |||
| 3 | Compare the expected value obtained in 2.b) with the population mean calculated in Group I - 1.a) | They have the same value | |||
| 4 | Check the theoretical expression: | ![]() | |||
![]() | |||||
| 5-a) | Percentiles of the sampling distribution of the estimator with the following orders: | ||||||
| i) 1.0% | i) 1.0%: 158.2 Kg | ||||||
| ii) 2.5% | ii) 2.5%: 205.5 Kg | ||||||
| iii) 3.5% | iii) 3.5%: 222.8 Kg | ||||||
| iv) 0.0% | iv) 50.0%: 540.7 Kg | ||||||
| v) 95.0% | v) 95.0%: 840.8 Kg | ||||||
| vi) 96.0% | vi) 96.0%: 856.7 Kg | ||||||
| vii) 97.5% | vii) 97.5%: 876.2 Kg | ||||||
| viii) 98.5% | viii) 98.5%: 901.0 Kg | ||||||
| 5-b) | Four intervals that encompass 95% of all possible sample means | Interval | Lower Limit | Upper Limit | |||
| From minimum value to 95th percentile | 83.3 | 840.8 | |||||
| From 5th percentile to largest value | 242.9 | 962.7 | |||||
| From 1st percentile to 96th percentile | 158.2 | 856.7 | |||||
| From 2.5th percentile to 97.5th percentile | 205.5 | 876.2 | |||||
| 8.3 | III | 5-c) | The width of the four intervals | Interval | Width | ||
| From minimum value to 95th percentile | 757.5 | ||||||
| From 5th percentile to largest value | 719.8 | ||||||
| From 1st percentile to 96th percentile | 698.5 | ||||||
| From 2.5th percentile to 97.5th percentile | 670.7 | ||||||
| 6 | The shortest of these intervals that holds 95% of all possible sample means | The last interval | |||||
| 7-a) | Probability of getting a sample of 3 landings with an average landing below or equal to 600 Kg | 62.5% | |||||
| 7-b) | Probability of getting a sample of 3 landings with an average landing above 600 Kg | 37.5% | |||||
| 7-c) | Probability of getting a sample of 3 landings with an average landing between 199 and 953 Kg | 96.7% | |||||
| 8-a) | l such that Prob { < l} = 0.95 | 840.8 Kg | |||||
| 8-b) | l1 and l2 such that Prob {l1< < l2} = 0.95 | l1=205.5 Kg l2=876.2 Kg | |||||
| 8.4 | I | 1-a) | Mean | 39.29 | |||
| 1-b) | Variance | 16.41 | |||||
| 1-c) | Standard deviation | 4.05 | |||||
| 2-a) | Estimate of population mean | 39.29 | |||||
| 2-b) | The estimator is biased? | No | |||||
| 2-c) | Sampling variance of ![]() | 4.10 | |||||
| 2-d) | Error of ![]() | 2.03 | |||||
| 2-e) | A 95% confidence interval of m | 35.32–43.26 | |||||
| 8.4 | II | 1 | A procedure to select a simple random sample of 4 numbered vessels | Select a whole random number between 1 and 20. Include the corresponding vessel in the sample. Repeat 4 times. If at any moment the vessel selected was already included in the sample, repeat the random number selection, until a new vessel is selected. |
| 2-a) | An estimator of the total amount of fish landed in the port during this day | N x Sample Mean | ||
| 2-b) | Sampling distribution of that estimator and the formulae to obtain the expected value and the expected sampling variance | Sampling Distribution: | ||
Ŷ N (E[Ŷ], V[Ŷ])E[Ŷ] = Y ![]() | ||||
| 3-a) | Estimate of total landing | 153.5 Kg | ||
| 3-b) | Estimate of sampling variance | 3923.4 | ||
| 3-c) | Estimate of error of the estimate | 62.6 Kg | ||
| 3-d) | A 95% confidence interval for the population total landings | 0–352.8 | ||
| 4 | Approximate size of the sample necessary to have an error 10% smaller than the one previously calculated in 3.c) | 5 | ||
| 8.4 | III | 1-a) | Proportion of females in the sample | 0.400 |
| 1-b) | Sample variance | 0.248 E[p]=P | ||
| 1-c) | Expressions for the expected value of p, and for the sampling variance of p | ![]() | ||
| 1-d) | Estimate of the sampling variance of p | 0.0058 | ||
| 1-e) | Estimate of the error of p | 0.0761 | ||
| 1-f) | Estimate of the 95% confidence interval for the proportion P applying the binomial distribution | 0.227–0.594 | ||
| 1-g) | Estimate of the 95% confidence interval for the proportion P applying the normal approximation to the binomial distribution | 0.251–0.549 | ||
| 2-a) | Estimate of total number of females in the population | 40 | ||
| 2-b) | Estimate of the sampling variance and of the error of the total number | V[Np]=57.93 SNp=7.61 | ||
| 2-c) | Estimate of the 95% confidence interval for the total number of females of the population applying the binomial distribution | 23 – 59 | ||
| 2-d) | Estimate of the 95% confidence interval for the total number of females of the population applying the normal approximation to the binomial distribution | 25 – 55 |
| 8.5 | I (landing ports) | 1 | Number of vessels to be sampled in each stratum | Class (stratum) | Sample Size |
| 100- | 2 | ||||
| 200- | 10 | ||||
| >300 | 4 | ||||
| Total | 16 | ||||
| 2-a) | Average landing per vessel in each category | Class (stratum) | Average Landing | ||
| 100- | 2 | ||||
| 200- | 6 | ||||
| >300 | 5 | ||||
| 2-b) | Variance between total landings within each stratum | Class (stratum) | Variance | ||
| 100- | 3.84 | ||||
| 200- | 19.18 | ||||
| >300 | 11.56 | ||||
| 3-a) | Estimates of mean landing for each stratum | Class (stratum) | Est. Mean Landing | ||
| 100- | 2 | ||||
| 200- | 6 | ||||
| >300 | 5 | ||||
| 3-b) | Estimates of expected sampling variance of the estimator of the mean for each stratum | Class (stratum) | Est. Exp. Var | ||
| 100- | 1.54 | ||||
| 200- | 1.54 | ||||
| >300 | 2.31 | ||||
| 3-c) | Estimates of error of the estimator of the mean for each stratum | Class (stratum) | Est. Error | ||
| 100- | 1.24 | ||||
| 200- | 1.24 | ||||
| >300 | 1.24 | ||||
| 8.5 | I | 3-d) | Estimates of total landing for each stratum | Class (stratum) | Est. Total Landing |
| 100- | 20 | ||||
| 200- | 300 | ||||
| >300 | 100 | ||||
| 3-e) | Estimates of expected variance of the estimator of total landing for each stratum | Class (stratum) | Est. Exp. Var. Total | ||
| 100- | 153.66 | ||||
| 200- | 3836.88 | ||||
| >300 | 924.80 | ||||
| 3-f) | Estimates of error of the estimator of total landing for each stratum | Class (stratum) | Est. Exp. Error Total | ||
| 100- | 12.40 | ||||
| 200- | 61.94 | ||||
| >300 | 30.41 | ||||
| 4-a) | Estimate of mean landing for total fleet | 5.25 | |||
| 4-b) | Estimate of expected variance of the estimator of the mean for total fleet | 0.77 | |||
| 4-c) | Estimate of error of the estimator of the mean for total fleet | 0.88 | |||
| 4-d) | Estimate of total landing for total fleet | 420 | |||
| 4-e) | Estimate of expected variance of the estimator of total landing for total fleet | 4915.34 | |||
| 4-f) | Estimate of error of the estimator of total landing for total fleet | 70.11 | |||
| 8.5 | II (surveys) | 1-a) | Estimate of index of total biomass of European hake for each stratum | Stratum | Est. Index (tonnes) |
| A1, 100–200 m | 129.8 | ||||
| A1, 200–300 m | 263.3 | ||||
| A1, 300–400 m | 1101.4 | ||||
| A1, 400–500 m | 289.2 | ||||
| A1, 500–600 m | 142.5 | ||||
| A2, 100–200 m | 764.0 | ||||
| A2, 200–300 m | 759.7 | ||||
| A2, 300–400 m | 239.7 | ||||
| A2, 400–500 m | 354.7 | ||||
| A2, 500–600 m | 319.4 | ||||
| 1-b) | Estimate of error of the estimator for each stratum | Stratum | Est. Error (tonnes) | ||
| A1, 100–200 m | 3.0 | ||||
| A1, 200–300 m | 7.6 | ||||
| A1, 300–400 m | 43.7 | ||||
| A1, 400–500 m | 9.9 | ||||
| A1, 500–600 m | 3.6 | ||||
| A2, 100–200 m | 20.6 | ||||
| A2, 200–300 m | 12.3 | ||||
| A2, 300–400 m | 7.6 | ||||
| A2, 400–500 m | 8.7 | ||||
| A2, 500–600 m | 10.2 | ||||
| 1-c) | Estimate of coefficient of variation of the estimator for each stratum | Stratum | CV Est. | ||
| A1, 100–200 m | 2.3% | ||||
| A1, 200–300 m | 2.9% | ||||
| A1, 300–400 m | 4.0% | ||||
| A1, 400–500 m | 3.4% | ||||
| A1, 500–600 m | 2.5% | ||||
| A2, 100–200 m | 2.7% | ||||
| A2, 200–300 m | 1.6% | ||||
| A2, 300–400 m | 3.2% | ||||
| A2, 400–500 m | 2.5% | ||||
| A2, 500–600 m | 3.2% | ||||
| 2-a) | Estimate of total biomass of European hake for the total area | 4 634 tonnes | |||
| 2-b) | Estimate of error of the estimator | 54 tonnes | |||
| 8.5 | II | 2-c) | Estimate of 95% confidence limits of the total biomass in the total area | 4 258 tonnes – 4 469 tonnes | ||
| 3-a) | Proportional allocation of the total 100trawls to the strata areas | Stratum | CV Est. | |||
| A1, 100–200m | 26 | |||||
| A1, 200–300 m | 10 | |||||
| A1, 300–400 m | 8 | |||||
| A1, 400–500 m | 7 | |||||
| A1, 500–600 m | 11 | |||||
| A2, 100–200 m | 16 | |||||
| A2, 200–300 m | 6 | |||||
| A2, 300–400 m | 4 | |||||
| A2, 400–500 m | 6 | |||||
| A2, 500–600 m | 6 | |||||
| Total | 100 | |||||
| 3-b) | Strata allocation that gives the maximum precision in the estimation of the total abundance | Stratum | Num. Hauls | |||
| A1, 100–200m | 3 | |||||
| A1, 200–300 m | 8 | |||||
| A1, 300–400 m | 29 | |||||
| A1, 400–500 m | 8 | |||||
| A1, 500–600 m | 3 | |||||
| A2, 100–200 m | 17 | |||||
| A2, 200–300 m | 13 | |||||
| A2, 300–400 m | 5 | |||||
| A2, 400–500 m | 7 | |||||
| A2, 500–600 m | 7 | |||||
| Total | 100 | |||||
| 8.6 | I (clusters) | 1 | 15 clusters selected with equal probabilities | Element | Cluster Nš | |
| 1 | 20 | |||||
| 2 | 35 | |||||
| 3 | 11 | |||||
| 4 | 25 | |||||
| 5 | 21 | |||||
| 6 | 27 | |||||
| 7 | 5 | |||||
| 8 | 28 | |||||
| 9 | 4 | |||||
| 10 | 13 | |||||
| 11 | 1 | |||||
| 12 | 10 | |||||
| 13 | 30 | |||||
| 14 | 7 | |||||
| 15 | 19 | |||||
| 8.6 | I | 2 | 15 clusters selected with probabilities proportional to the cluster sizes | Element | Cluster No. | |
| 1 | 10 | |||||
| 2 | 11 | |||||
| 3 | 20 | |||||
| 4 | 23 | |||||
| 5 | 9 | |||||
| 6 | 25 | |||||
| 7 | 14 | |||||
| 8 | 35 | |||||
| 9 | 24 | |||||
| 10 | 28 | |||||
| 11 | 12 | |||||
| 12 | 29 | |||||
| 13 | 27 | |||||
| 14 | 34 | |||||
| 15 | 22 | |||||
| 8.6 | I | 3 | 15 clusters selected by selecting 3 clusters from each province with probabilities proportional to the sizes of the clusters of each stratum | Element | Prov | Cluster No. |
| 1 | 1 | 3 | ||||
| 2 | 1 | 7 | ||||
| 3 | 1 | 1 | ||||
| 4 | 2 | 10 | ||||
| 5 | 2 | 11 | ||||
| 6 | 2 | 9 | ||||
| 7 | 3 | 17 | ||||
| 8 | 3 | 16 | ||||
| 9 | 3 | 18 | ||||
| 10 | 4 | 20 | ||||
| 11 | 4 | 23 | ||||
| 12 | 4 | 25 | ||||
| 13 | 5 | 35 | ||||
| 14 | 5 | 28 | ||||
| 15 | 5 | 29 | ||||
| 8.6 | II | 1-a) | Number of clusters in the population | 23 | ||
| 1-b) | Number of clusters in the sample | 5 | ||||
| 1-c) | Number of elements in cluster 14 | 50 | ||||
| 2-a) | Sample mean value per cluster | 1294.6 | ||||
| 2-b) | Sample mean value per element | 25.9 | ||||
| 2-c) | Sample variance between clusters | 1422.8 | ||||
| 3-a) | Estimate of the expected value of the estimator | Estimator: N * Mean Value per Cluster Est. Expected value: 29 775.8 | ||||
| 3-b) | Estimate of the sampling variance of the estimator | 222.7 | ||||
| 3-c) | Estimate of the error of the estimator | 14.9 | ||||
| 8.6 | III | 1-a) | Estimate of the total value of the population | 19 915.4 | ||
| 1-b) | Estimate of the error of your estimator | 32.4 | ||||
| 2-a) | Estimate of the total landing of all the vessels | 21 205 | ||||
| 2-b) | Estimate of the sampling variance of your estimator and its error | Sampling Var Sampling Error | 38 482 456 6 203 | |||
| 2-c) | Estimate of an approximate 95% confidence interval of the total landing | 3 981–38 428 | ||||
| 8.7 | I | 1-a) | Estimate of the total weight of fish landed | 248 785 | ||
| (two | 1-b) | Estimate of the error of the estimation | 48 003 | |||
| stages) | 2-a) | Estimate of the proportion of boxes of fish in the total landings | 0.228 | |||
| 2-b) | Estimate of the error of the estimation | 0.053 | ||||
| 8.7 | II | 1 | Estimate of the total weight of fish landed | 192 090 | ||
| 2 | Estimate of the error of the estimation | 50 285 | ||||