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Unformatted text preview: CHAPTER 10 BASIC STATISTICAL MEASURES EXERCISE 10.1 Section 10.1 Populations and samples (page 9) 1. (a) Population: water consumption of every family in Hong Kong Sampling units: households or dwelling units (b) Population: all the voters Sampling units: households or voters (c) Population: all the monthly sales records of the company Sampling units: monthly sales accounts (d) Population: all the sewing machines in all garment factories Sampling units: garment factories 2. (a) Population: heights of all the newborn babies in Hong Kong Sampling units: newborn babies in Hong Kong (b) A population parameter is the average of the population. (c) The population is infinite. The exact value of the population average suggested in (b) cannot be found. (d) (i) The average of the 30 readings will be used to estimate the population average. (ii) No. The sample is not a random sample and sample statistics derived from it may depend on the characteristics of the hospital (e.g. admission policy, location). Also, the sample is not large enough. 3. (a) Population: prices of all the DVD movie “Crouching Tiger and Hidden Dragon” in the market Sampling units: Outlets selling those DVDs (b) A population parameter is the minimum of the population. (c) (i) The minimum price of the movie offered by the 50 retail stores is a sample statistic that can be used to estimate the population minimum. (ii) No. The sample is not a random sample. 4. (a) Let all the Secondary 6 students in the school be classified as ‘ S ’ (needing spectacles) or ‘ N ’ (not needing spectacles). Then the population under investigation is the collection of the S ’s and N ’s of all those Secondary 6 students. (b) (i) Let all the students in the school be classified as ‘ S ’ or ‘ N ’, as defined in (a) . Then the population under investigation is the collection of the S ’s and N ’s of all the students in the school. (ii) The proportion found is an estimate of the population proportion of the population defined in (b)(i) . 1 C HAPTER 10 B ASIC S TATISTICAL M EASURES (iii) The estimate cannot be accurate. It should be biased because usually the proportion of students who need to wear spectacles when reading the blackboard is higher in senior classes than in junior classes. 5. (a) Population: diameters of all trees on the plateau Sampling units: the N small regions (b) The required parameter is the total number τ of trees with diameters exceeding 30 cm. (c) Sample statistic = N × average of s ' i t in the sample = ∑ × n i i t n N 1 = 1 6. Discard the leading zero of the given random numbers and read off the digits in twos along the rows. The resulting 2-digit random numbers are: 29 85 26 06 77 93 68 35 03 78 31 44 23 33 08 64 47 90 21 48 40 61 32 85 Then take the first 8 of the above numbers which are less than 80, i.e. 29 26 6 77 68 35 3 78 Finally, add 930 000 to each of them to get the invoice numbers which are included in the sample....
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