MTN Eswatini .ill (@)' $ 11% 09:06 QUESTION ONE [48] SECTION A: MULTIPLE-CHOICE QUESTIONS: FIVE alternatives are provided for each of the following questions. Choose the correct alternative for each of the questions/statement. Write down the question number and the alphabet corresponding to your choice next to the question number. Example: 1.13 B (12 X 4) 1.1. Which one of measures of dispersion is not affected by outliers? A. Coefficient of variation B. Interquartile range C. Standard deviation D. Range E. None of the above. 1.2. Which of the following could indicate that a dataset is skewed? A The range is equal to 5 standard deviations B. The range is larger than the interquartile rage C. The mean is much smaller than the median D. There are no outliers. E. None of the above. 1.3 What level of measurement data is associated with the least sophistication in terms of the statistical analysis that can be done with the data: A Nominal measurement B. Ordinal measurement C. Interval measurement D. Ratio measurement E. None of the above. 1.4. Random variables which yield numeric responses and can be meaningfully manipulated using conventional arithmetic operations is typically referred as... A. Quantitative data B. Qualitative data C. Questionnaire D. Independent variable E. None of the above. 1.5. Read the statement below and answer the question that follows: In this type of sampling design, every member of the population has similar chance of being selected as a study subject. Which one of the following methods of sampling best fits the description above? > A. Simple random sampling. B. Stratified sampling. C. Cluster sapling.. D. Systematic sampling. E. None of the above. 1.6. A student initially recruited nine (9) participants for a pilot study. However, he wa advised by his supervisor to add an additional participant to the pilot study. If mean age of the nine participants is 34 years and the mean of the ten partic 35.2, what is the age of the tenth participant? A. 40.5 years OMTN Eswatini .ill 11% 09:06 1 In this type of sampling design, every member of the population has similar chance of being selected as a study subject. Which one of the following methods of sampling best fits the description above? A. Simple random sampling. B. Stratified sampling. C. Cluster sapling.. D. Systematic sampling. E. None of the above. 1.6. A student initially recruited nine (9) participants for a pilot study. However, he was advised by his supervisor to add an additional participant to the pilot study. If the mean age of the nine participants is 34 years and the mean of the ten participant is 35.2, what is the age of the tenth participant? A. 40.5 years B. 46.0 years C. 38.5 years D. 64.5 years E. None of the above. 1.7. Which one of the following sampling examples would generally lead to the least reliable statistical inferences about the population from which the sample has been selected? A. A random sample selected without replacement. B. A random sample selected with replacement. C. A voluntary response sample. D. A systematic sample. E. None of the above. N > > 1.8. Refer to the less-tan ogive below for the duration of international call and answer question that follows: Duration of International Calls 70 163 164 CMTN Eswatini .ill 11% 09:06 1.8. Refer to the less-tan ogive below for the duration of international call and answer question that follows: Duration of International Calls 70 163 64 - 50- Number of Calls 125 8 16 24 32 40 48 Duration (minutes) The percentage of calls that are longer than 24 minutes is: A. 78.125%. B. 50%. C. 21.875%. D. 37.5%. m None of the above. 1.9. Which one of the following statements about the distinction between cluster sampling and stratified sampling is patently false? A. In a cluster sampling a sample of mutually exclusive naturally-occurring subgroups within the population or clusters is chosen using an appropriate procedure, and a complete enumeration of only the selected clusters is carried out; in stratified sampling, the sampling is done on elements within each stratum. B. The main objective of stratified sampling is to increase precision and representation, whereas the objective of cluster sampling is to reduce costs and improve sampling efficiency. C. In stratified sampling, the sampling is done on elements within each stratum. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are sampled. D. In stratified sampling the subgroups of interest are naturally occurring, whereas in cluster sampling the researcher imposes the bifurcation of the subgroups. E. None of the above. Questions 1.10. - 1.12 refer to the table below that shows how life expectancy is relat levels of pollution in the environment. In a study, the life expectancy (in year) of 6 countries CMTN Eswatini .will 11% 1 09:06 C. In stratified sampling, the sampling is done on elements within each stratum. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are sampled. D. In stratified sampling the subgroups of interest are naturally occurring, whereas in cluster sampling the researcher imposes the bifurcation of the subgroups. E. None of the above. Questions 1.10. - 1.12 refer to the table below that shows how life expectancy is related to levels of pollution in the environment. In a study, the life expectancy (in year) of 6 countries was obtained, along with the level of pollution. The results are shown in the table below: Country Cost (rand' 000) Circulation South Afri 8 65 ndia 40 60 Sweden 2 80 Belgium 5 75 Venezuela 22 70 China 38 64 1.10. The calculations of the person correlation coefficient for the above data are: A. Sxy = -508; Sxx = 280; Syy = 1416.833; r= -0.807 B. Sxy = -508; 5xx = 1416.833; Syy = 280; r= -0.807 C. Sxy = 570; Sxx = 1416.833; Syy = 280; r = 0.905 D. Sxy = 570; Sxx = 280; Syy = 1416.833; r = 0.897 E. None of the above. 1.11. Based on the correlation coefficient obtained, which one of the following statements correctly describes the relationship between the 'life expectancy' and levels of pollution in the environment"? A The 'life expectancy' and levels of pollution in the environment' are very strongly, positively correlated. B The 'life expectancy' and levels of pollution in the environment' are very strongly, inversely correlated. C The 'life expectancy' and levels of pollution in the environment' are weakly, positively correlated. > > D The 'life expectancy' and levels of pollution in the environment' are moderately, negatively correlated. E. None of the above. 1.12. The linear regression equation is: A. y = 75.872 - 0.3585X B. y = 75.872 + 0.3585X C. Y= 144.3524 - 1.814 X D. Y= 144.3524 + 1.814 X E. None of the above. SECTION B QUESTION TWO [22] O OMTN Eswatini .ill 11% 09:07 D The 'life expectancy' and levels of pollution in the environment' are moderately, negatively correlated. E. None of the above. 1.12. The linear regression equation is: A. y = 75.872 - 0.3585X B. y = 75.872 + 0.3585X C. Y= 144.3524 - 1.814 X D. Y= 144.3524 + 1.814 X E. None of the above. SECTION B QUESTION TWO [22] A hardware shop recorded its daily turnover for 100 trading days as shown in the table below Daily Turnover Number of days [250, 500) 5 500 , 750) 8 750 ,1000) 11 [1000 , 1250) 30 [1250, 1500) 32 [1500, 1750) 14 TOTAL 10 2.1 Using appropriate computational formulae calculate the: 2.1.1 average daily turnover of the hardware shop. (3) 2.1.2. median daily turnover of the hardware shop. (3) 2.1.3 modal daily turnover of the hardware shop. (3) 2.1.4 standard deviation (6) 2.2. Determine the maximum daily turnover associated with the lowest 25%. (4) 2. 3. what daily turnover separates the highest 25% of turnover days from the rest? (4) UT QUESTION THREE [15] The information on 300 employees of a small manufacturing company on the basis of age and work category is presented in a table below > > Work category Age production Sales office Under 25 50 2 50 25 and under 40 70 24 50 Above 40 40 10 If an employee is selected at random what is the probability that the employee is: 3.1 between 25 and 40 years of age 3.2 a production worker is 3 3 given that he/she is an office worker OMTN Eswatini .will 11% 09:07 QUESTION THREE [15] The information on 300 employees of a small manufacturing company on the basis of age and work category is presented in a table below Work category Age production Sales office Under 25 50 2 50 25 and under 40 70 24 50 Above 40 40 10 If an employee is selected at random what is the probability that the employee is: 3.1 between 25 and 40 years of age (3) 3.2 a production worker is (3) 3.3 over 40, given that he/she is an office worker (4) 3.4 NOT under 25 or is a production worker (5) QUESTION THREE [15] The table below displaying the average price (R) and average quantity (kg) for three (3) products in three-year period from 2019 to 2021. ITEM Milk Butter Cheese 2019 3.95 61.5 34.8 Price (R) 2020 3.89 62.2 35.4 2021 4.13 59.7 38.9 2019 9675 117.7 77.93 Quantity (millions kg) 2020 9717 115.5 74.39 2021 10436 115.5 82.79 The using 2019 as base year calculate the: 4.1 Laspeyres price and quantity indices for the year 2021 and interpret your results. (10) 4.2 Paasche price and quantity indices for the year 2020. (5) END OF QUESTION PAPER 7 of 11 O O