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QuotaSamplingPopulation100000Quota5Number of people to be surveye.docx
- 1. QuotaSamplingPopulation100000Quota5%Number of people to be surveyed in each categoryMale 55%Female 45%Social classABCABCAge30%50%20%30%50%20%TOTAL16- 2925%30 - 4430%45 - 6430%65 and over15%TOTAL RandSampleIllustration of simple random samplingSummary statisticsMeanStdevPopulationSamplePopulationFamilyIncomeR andom#FamilyIncome Random#1$25,4712$26,0593$20,3534$22,3535$26,2946$26,824 7$25,1188$21,7069$22,58810$19,82411$25,94112$30,29413$2 1,11814$20,94115$25,29416$22,70617$19,05918$13,47119$28, 29420$18,76521$33,17622$19,76523$22,41224$25,00025$26,4 1226$20,70627$35,76528$25,00029$28,00030$21,23531$19,41 232$18,64733$28,58834$23,11835$19,41236$21,35337$16,706 38$27,58839$21,94140$24,118 Illustration of Random Sampling StratifiedSamplingStratified sampling by TesBuryTotal sample size100Strata based on ageStratum 118to30Stratum 231to62Stratum 363to80CustAgeCategoryCust_1Age_1Cust_2Age_2Cust_3Age_ 31492393554665526377348349331036112312631324144715301 65917311834193520292147223123542441253826302744283729 32304131483236333634263556363637533875393540644134427 14325444545364635473148434941506251365255536354575525 56285739585659586021613362286349647165376652672768666 95270377143724373427446753676317736786279308029814082 43834584398561863187238852893890409157923893419452956 49636974598379926100461012210276103441043210543106341 07361085810937110441114011255113521143111546116251176 31185811925120381214912227123581242212542126381276712 87112947130741312813234133251344913558136591375713863 13937140421414714233143411444014553146451474714841149 67150341512815255153401544215561156401574315855159521 60381614816230163301644916557166261674716872169461702
- 4. 93458935389365393737938579393194049941319423894334944 47945359465294739948479495395049951629523395342954489 55499565995736958339595596057961409624596365964279656 19664296739968399693897041971329723697341974549753597 63597746978389794098035981549823698364984619854398636 98751988439893799046991569924199341994339953399653997 639983099950100026 MS1023 Business Statistics with Computer Applications I Sampling with Excel Dr Maho Sonmez /[email protected]/ 1 SAMPLING STRATEGIES: ILLUSTRATIONS ON EXCEL 1) Devising a quota sampling using Excel This was the example used in the lecture. Suppose that you are asked to find out the opinions of the residents in a small county about the location of a supermarket in the outskirts of the city. No sampling frame is available. But we can get the data we want from the county about the gender, age group & social class. You think as an experienced analyst 5% quota for each group is enough to get an overall opinion of the residents.
- 5. Total number of residents: 100000 Gender as % of population: 55% Male, 45% Female Age groups as % of population: 16-29 (25%); 30-44 (30%); 45-64 (30%); 65+ (15%) Social Class as % of population: A (30%); B (50%); C (20%) Devise a quota sampling for this example using Excel. Do the following: (i) Download the Excel file entitled “SamplingWithExcel” from Blackboard to your user space (or to a USB). (ii) Start Excel and open the worksheet “QuotaSampling”. (iii) Use relative or absolute references to the cells (where necessary) to enter appropriate formulae to calculate the number of people to be surveyed in each category.
- 6. MS1023 Business Statistics with Computer Applications I Sampling with Excel Dr Maho Sonmez /[email protected]/ 2 2) Illustration of Simple Random Sampling using Excel This example is adapted from Albright, Winston and Zappe (p.380). Consider the frame of 40 families (as Population) with annual incomes shown in the worksheet “RandSample” in the file “SamplingWithExcel”. We want to choose a simple random sample of size 10 from this frame. How can this be done? And how do summary statistics of the chosen families compare to the corresponding summary statistics of the population? Our objective is to illustrate how Excel’s random number function, RAND(), can be used to generate simple random samples.
- 7. (i) Start Excel and open the file “SamplingWithExcel”. Select “RandSample” worksheet. (ii) Select cell B5 and enter the formula =AVERAGE(B10:B49) (iii) Select cell C5 and enter the formula =STDEVP(B10:B49) (iv) Select cell C10 and enter the formula =RAND() (v) Copy the formula in cell C10 down to cells C11 to C49. WARNING: Excel’s RAND() function is sensitive in the sense that whenever you do something else on the worksheet such as copy a formula or enter a formula, Excel generates new set of random numbers. So if this happens, don’t panic! (vi) Now, you should be able to see generated random numbers. Now, to enable sorting we must “freeze” the random numbers (see warning in (v)). In other words, we must replace the formulas with their values. To do this, select and copy the range C10:C49, and then select C10, right click and select Paste Special. Then, check the Values option and click OK. (vii) Now, copy the range A10:C49 to the range E10:G49.
- 8. (viii) To select a random sample of 10 families, you may do the following. Select G10 and click the Sort button, i.e. . Then, the 10 smallest random numbers are the ones in the sample. (ix) Type in the formulas =AVERAGE(F10:F19) to cell B6 and =STDEV(F10:F19) to C6. Observe and compare the population statistics with the sample statistics. (x) For info only. To obtain more random samples of size 10 (for comparison), we need to go through the above process repeatedly. MS1023 Business Statistics with Computer Applications I Sampling with Excel Dr Maho Sonmez /[email protected]/ 3 3) Stratified Sampling using Excel This example is adapted from Albright, Winston & Zappe (p 387).
- 9. The worksheet “StratifiedSampling” contains a frame of all 1000 people in the city of Loveboro who has TesBury credit cards. TesBury is interested in estimating the average number of credit cards these people own, as well as other information about their use of credit. The company decides to stratify these customers by age, select a stratified sample of size 100 with proportional sample sizes, and then contact these 100 people by phone. How might TesBury proceed? Our objective is to illustrate how stratified sampling, with proportional sample sizes, can be implemented in Excel. REASONING & ASSUMPTIONS: TesBury has to decide exactly how to stratify by age. Their reasoning is that different age groups have different attitudes and behaviour regarding credit. After some preliminary investigation and discussions, they decide to use three age
- 10. categories: 18-30, 31-62, and 63-80. It was assumed that no one in the population is younger than 18 or older than 80. (i) You need to work on the worksheet “StratifiedSampling” in the Excel file “SamplingWithExcel”. (ii) Start Excel and open the file “SamplingWithExcel”. Select “StratifiedSampling” worksheet. (iii) As you can see from the worksheet, we have a list of 1000 customers (numbered in ascending order) and the ages of these customers. We also know that there are three strata based on age. Our first task is to find out which age stratum each customer is in. To do this, we will assign number 1 if the customer is aged between 18 and 30; number 2 those customers aged between 31-62 and 3 for those between 63 and 80. We could do this manually but you can imagine how tedious and time consuming this can be
- 11. for 1000 entries. We can do this with one formula. How? Follow the instructions below. (iv) Select cell C11. We must use the IF Logical function here. The logic is as follows, if it is true that cell B11 is less than or equal to 30, than number 1 should appear in C11; if it is true that cell B11 is less than or equal to 62, than number 2 should appear in C11; otherwise number 3 should appear in MS1023 Business Statistics with Computer Applications I Sampling with Excel Dr Maho Sonmez /[email protected]/ 4 cell C11. Enter the formula =IF(B11<=D6,1,IF(B11<=D7,2,3)) in cell C11 and then copy it down column C. Did you notice that the results are not as expected? Why? Hint: RELATIVE or ABSOLUTE references. (v) By now, you should have entered the correct formula and each customer is
- 12. assigned a category number. Now, we need to “unstack” the data into three groups, one for each category as can be seen from columns F through M. For example, columns F and G will list the customer numbers and ages for all customers in the first age category (i.e. 18-30). To do this, select C11 and click on (A-Z ascending) sort button. Then, copy the range of customers and their ages who are in the first age category and select F11 and paste. Repeat the same for categories 2 and 3. (vi) Type Counts in Cell F5 and SampSize in Cell G5. Select F6 and enter the formula =Count(F11:?) where ? is the last cell (or customer) in the first age category. Repeat this to get the number of customers in the age categories 2 and 3 in cells F7 and F8. (vii) We need to find out how many customers should be selected from each
- 13. category to make up the total sample size of 100. TesBury decided to use a proportional sample size. So select G6 and enter the formula =ROUND($C$3*F6/1000,0) to calculate the number of customers to be selected in the first age category. Copy the formula in Cell F6 to get the number of customers for age categories 2 and 3. Hence, TesBury should sample 13, 77, and 10 customers from three age categories. (viii) Now, the next question is how to select 13, 77, and 10 customers from three age categories. The answer is simple, use the simple random sampling process explained earlier. (ix) Type Random# to cells H10, K10 and N10. Now, select H11 and enter formula =Rand() and copy it down. “Freeze” these random numbers with the Copy and Paste Special/Values commands. Then, copy the whole category 1 (i.e. select F10:H10 to down). Paste them to cell P10. Select
- 14. any cell under Random# and click on sort button (ascending A-Z). Then, select the top 13 customers. (x) Repeat above process to select customers for the age categories 2 and 3.