Question 13 Marks
Draw a random sample of size $5$ $(i)$ with replacement $(ii)$ without replacement from a population of $50$ units using the following $15$ two digit random numbers: $62, 25, 6, 60, 95, 55, 98, 11, 71, 25, 20, 45, 89, 27, 40$
AnswerWe shall first assign numbers $1$ to $50$ to the $50$ units of the the population.
Since the size of the population is $50$ , we shall ignore random numbers which are greater than $50$ . So we are left with random numbers : $25,6,11,25,20,45,27$ and $40$ .
$(i)$ As the sample has to be selected with replacement, we shall not ignore the random numbers which are repeated more than once. As we require random sample of size $5$ , we shall select first $5$ random numbers. The selected random numbers are: $25,6,11,25$, and $20$.
$(ii)$ As the sample has to be selected without replacement, we shall ignore the random numbers are repeated more than once. As we require raddom sample of size $5$ , we shall select first $5$ random rs. The selected random numbers are: $25,6,11,20$, and $45$ . (as $25$ cannot be selected again)
View full question & answer→Question 23 Marks
Write a note on systematic sampling.
Answer
- In systematic sampling, the first sample unit is rendomly selected and the remaining units of the sample are automatically selected in definite sequence at uniform interval from the list of population units.
- If the complete list of population units arranged in some systematic manner is available. Then this method of sampling is advisable.
- Suppose, $N$ units of the population are arranged in some systematic manner and numbered $1$ to $N.$ A sample of size $n$ is to be drawn. Then sampling interval $k =\frac{N}{n}$; where $k$ is a positive integer is determined and a random number is selected from first $k$ units of population and select
- every $k$ th unit therefore. Set of such selected units is called systematic sample and the method of obtaining such a sample is called systematic sampling.
Illustration:
- If the random number selected from the first $k$ unit is $4$, then the units at order $4, 4+k, 4+ 2k, 443k, ...,$ etc. of the list of population units form the systematic sample.
View full question & answer→Question 33 Marks
State the disadvantages of stratified random sampling.
AnswerThe disadvantages of stratified random sampling are as follows :
$(1)$ it is difficult to divide the population into homogeneous strata.
$(2)$ If stratification is not proper, accuracy of the results obtained by this method decreases.
$(3)$ The procedure of estimating population parameters in more complicated as compared to simple random sampling.
View full question & answer→Question 43 Marks
Write a note on stratified random sampling.
Answer
- If the population is hetrogeneous, then simple random sample cannot be a representative sample of the population.
- In this situation, by using the stratified random sampling stratified random sample is be selected.
- In this method, first of all units of population are divided into different strata of homogeneous nature.
- All these strata are different among themselves but are internally homogeneous.
- Now, a random sample is taken from each stratum and random samples so obtained from all strata are combined to get a sample which is called a stratified random sample and the method of selecting such a sample is called stratified random sampling method.
Illustration :
- Suppose out of $600$ families in an area of a city, $200$ families are having less Income, $300$ families are having average Income and $100$ families are having more Income.
- For socio - economic survey of these families sample of $60$ families is to be selected.
- Taking the families of different income groups as strata families are randomly selected from each stratum in the proportion of $200 : 300 : 100$. In this way.
- $20$ families having less income.
- $30$ families having average income and $10$ families having more.
- Income are selected at random and the sample of $60$ families so obtained is known as stratified random sample.
- In stratified random sampling the population is divided into different strata so each stratum gets representation.
- Hence the representative sample can be obtained for all the characteristics of the population.
- The work of selecting samples from different strata can be assigned to separate investigators or enumerators and hence administrative convenience can be improved.
- If proper care is not taken while dividing the population into different strata, then appropriate representative sample of the population cannot be obtained and therefore the reliability of results can be reduced.
View full question & answer→Question 53 Marks
Write a note on simple random sampling.
Answer
- A sampling in which every unit of the population has an equal chance of being selected in the sample, is called a simple random sampling, This method is considered to be superior to all other methods of sampling, because.
- In this method there is no place for personal bias or prejudice for any unit of the population.
- The selection of each unit of sample is done independently, i.e., the selection of any unit does not depend upon the selection of any other unit.
- Which unit of the population will be selected in the sample is not decided in advance.
- In this method the selection of sample units being done randomly, it is called simple random sample, which appropriately represents the population.
- The data of the sample units selected by this method gives reliable estimates of the population values.
- When the size of the population is large and the variation among the units of the population for any characteristics is more then the sample obtained by this method cannot give the reliable results.
View full question & answer→Question 63 Marks
State the advantages of simple random sampling.
AnswerAdvantages of simple random sampling method are as follows :
$(1)$In simple random sampling each unit of the population has an equal chance of being selected in the sample.
$(2)$ In this method the selection of sample being done without any bias or prejudice.
$(3)$ For Homogeneous population, the sample obtained by this method shows good representation of population and hence reliable results can he obtained.
$(4)$ In this method, from the sample data, reliable information about the characteristics of the population can be obtained with less cost and time.
View full question & answer→Question 73 Marks
State the points to be considered while determining the sample size.
AnswerThe following points should be taken into account while determining the sample size:
$(1)$ The purpose of the inquiry,
$(2)$The size and scope of the population,
$(3)$ Availability of time, monetary resources and technical expertise.
$(4)$ The variation among the values of a variable quantity of the units of population $(heterogeneity of population)$ and
$(5)$ Expected level of accuracy.
View full question & answer→Question 83 Marks
State the characteristics of an ideal sample.
AnswerAn ideal sample must possess the following characteristics :
$(1)$ it should be representative of the population.
$(2)$Its selection should be made without any kind of prejudice or bias. That is. its selection should be made at random.
$(3)$ The selection of the units of a sample should be made during the same duration of time.
$(4)$ Selection of sample units should be independent.
$(5)$ It should be of appropriate size.
View full question & answer→Question 93 Marks
A Teacher wants to check home – work of $10$ students out of $30$ students of Standard $XI$ of a school. How many random samples can be obtained using systematic sampling ?
Answer
- Here. $N=30 ; n=10$
- $\therefore k =\frac{30}{10}=3$
- $K=3$, therefore selected possible random number may be $1,2$ or $3.$
- If selected random number is $1:$
- Sample $1: 1,4,7,10,13,16,19,22,25,28$
- If selected random number is $2:$ Sample $2: 2,5,8,11,14,17,20,23,26,29$
- If selected random number is $3:$ Sample $3: 3,6,9,12,15,18,21,24,27,30$
View full question & answer→Question 103 Marks
Differentiate population inquiry and sample inquiry :
Answer
| |
Population Inquiry |
|
Sample Inquiry |
| $1.$ |
In population survey all units are examined. Hence it requires more time. |
$1.$ |
In sample survey few units are examined. Hence it requires less time. |
| $2.$ |
The cost of survey is more. |
$2.$ |
The cost of survey is less. |
| $3.$ |
As more units are to be examined proper accuracy cannot be maintained. |
$3.$ |
Accuracy can be maintained as few units are to be examined. |
| $4.$ |
Population study is not possible when the units are to be destroyed during the study. |
$4.$ |
Sample study can be used when the units are to be destroyed during the study. |
| $5.$ |
AS more persons are to be employed in the work experts may not be available. |
$5.$ |
As few persons are to be employed, experts may be available. |
| $6.$ |
As more units are tobe studied the work becomes tedious. |
$6.$ |
As few units are to be studied the work is relatively easy. |
| $7.$ |
As all units are examined complete information is available. |
$7.$ |
Limited number of units are examined hence complete information is not available. |
View full question & answer→Question 113 Marks
Select all possible samples of size $4$ using systematic sampling from a population of $20$ units.
Answer
- Here, $N=20 . N=4, k=\frac{20}{4}=5$
- We have to select all possible systematic samples of size $4 . K=5$. Therefore, selected possible random number may be $1,2,3,4$ or $5.$
- If selected random number is $1:$ Sample $1: 1,6,11,16$
- If selected random number is $2:$ Sample $2: 2,7,12,17$
- If selected random number is $3:$ Sample $3: 3,8,13, 18$
- If the selected random number is $4:$ Sample $4: 4,9,14,19$
- If the selected random number is $5:$ Sample $5: 5,10,15,20$
View full question & answer→Question 123 Marks
There are $60$ employees in the office of an $I.T.$ company. $5$ employees are to be selected using systematic random sampling for a trial of ‘work from home’ concept. Explain how can a sample be selected ?
AnswerHere, $N=60 ; n=5$
Sample interval $k=\frac{N}{n}=\frac{60}{5}=12$
Assign numbers $1$ to $60$ to the employees of an $IT$ company.
Select a random number in sample interval $1$ to $12.$
Suppose, the selected number is $7$ .
Select every $12$th number from $7$th. Such four numbers are to be selected.
The sample unit at $7,19,31,43$ and $55$ will form a sample of employees.
View full question & answer→Question 133 Marks
To study the usages of fertilizer, randomly select $10$ farmers without replacement from $30$ small farm owners and $20$ large farm owners. There should be $6$ small farm owners and $4$ large farm owners in the randomly selected $10$ farmers.
Random numbers for small farm owners : $2, 95, 18, 96, 20, 84, 56, 11, 52, 03, 10, 45.$
Random numbers for large farm owners : $04, 40, 34, 11, 72, 11, 50, 55, 08, 13, 76, 18.$
AnswerSmall farm owners: $N = 30, n = 6$
Ignoring random numbers greater than $30$ and the repeated numbers, the selected random numbers are :
$12, 18, 20, 11, 03, 10$
- Hence, the numbers of sample units of the sample of $6$ small farm owners are : $12, 18, 20, 11, 03, 10$
Large farm owner : N = 20, n = 4
- Ignoring random numbers greater than $20$ and the repeated numbers, the selected random pumbers are: $04, 11, 08, 13, 18$
- Hence, the number of sample units of the sample of $4$ large farm owners are : $04, 11, 08, 13, 18$. Thus. randomly selected $10$ farmers are : Small farm owner: $12, 18, 20. 11, 03, 10$ Large farm owner : $04, 11, 08, 13.$
View full question & answer→Question 143 Marks
Draw a random sample of $2$ per cent “students without replacement from $600$ students of a particular college for giving their feedback on faculty members. There are $200$ students in each of the three years ($F.Y., S.Y.$ and $T.Y.$)
Use the following three-digit random numbers :
For $F.Y. : 158, 092, 411, 745, 009, 724, 674, 550, 716, 359, 419, 696, 200, 458.$
For $S.Y.:384, 019, 679, 131, 390, 057, 299, 786, 006, 206, 729, 344, 543, 309.$
For $T.Y.: 227, 483, 741, 766, 027, 070, 648, 956, 198, 912, 200, 058, 696, 500.$
Answer
- Here, $N =600$
- $2 \%$ sample without replacement is to be obtained. Therefore. $n =600 \times \frac{2}{100}=12$.
- First stratum :
- $F.Y. : N _1=200, n _1=200 \times \frac{2}{100}=4$
- Ignoring the random numbers greater than $200$ and the repeated numbers, the selected random numbers are: $158 , 092, 009, 200.$
- Hence, the number of the sample units of sample of $4$ students of First year are: $158, 009, 200.$
- Second stratum:
- $S.Y.: N _2=200, n _2=200 \times \frac{2}{100}=4$
- Ignoring the random numbers greater than $200$ and the repeated numbers. the selected random numbers are : $019,$ $131,057,006$.
- Hence, the number of the sample units of the sample of $4$ students of $S.Y$. are : $019,131,057,006$.
- Third stratum:
- $T.Y. : N_2=200, n_3=200 \times \frac{2}{100}=4$
- Ignoring the random numbers greater than $200$ and the repeated numbers, the selected random numbers are : $027$ , $070,198,200,058$.
- Hence, the random number of the sample units of the sample of $4$ students of Third year are : $027, 070, 198, 200.$
View full question & answer→Question 153 Marks
Three-digit random numbers are given below :
$170, 111, 352, 002, 563, 203, 405, 545, 111, 446, 776, 691, 816, 233, 616, 300, 250, 816, 010.$
Using the random numbers, select a $2 \%$ random sample with and without replacement from a population of 350 units.
Answer
- First of all we will assign numbers to 350 to the units of population.
- Population size is $N = 350$, a three-digit number. Hence, the random numbers greater than 350 are ignored.
- The selected random numbers are : $170, 111, 002, 203, 111, 233, 300, 250, 010.$
- $2\%$ means $350x$
$= 7$ units are to be selected in the sample.
Sample with replacement :
- Considering the repeated numbers, first seven random numbers are : $170, 111, 002, 203,111, 233, 300.$
- Thus sample with replacement consists of the random numbers $170, 111, 002, 203, 111, 233, 300.$
Sample without replacement : Ignoring the repeated numbers, the first seven random numbers are: $170, 111, 002, 203, 233, 300, 250.$
- Thus, sample without replacement consists of the random numbers $107, 111, 002, 203, 233, 300, 250.$
View full question & answer→Question 163 Marks
There are $70$ students in a class room. A teacher wants to select $7$ students for $7$ activities. Obtain a random sample with replacement using the following random numbers :
$274, 323, 923, 599, 667, 320, 910, 484, 786, 253, 009, 885, 115.$
Answer
- First of all, we will assign numbers $1$ to $70$ to the students in a classroom.
- Population size $N= 70$, a two-digit number. Hence, we consider only first two digits of random numbers and ignore the first two digits greater than $70.$
- Random sample with replacement is to be obtained. Hence, we consider the repeated random numbers.
- The selected random numbers are: $27, 32, 59, 66, 32, 48, 25, 11.$
- A random sample of $7$ students is to be obtained. Therefore we select first seven random numbers from the above.
- Thus, random numbers of selected seven students are respectively $27, 32, 59, 66, 32, 48, 25$. which is random sample with replacement.
View full question & answer→Question 173 Marks
Use the following random numbers to select a random sample of $5$ $ATMs$ without replacement from a total of $100$ ATMs of a bank :
$018, 502, 153, 096, 027, 007, 118, 245, 012, 054, 444, 211, 323, 428, 137.$
Answer
- First of all, we will assign numbers $1$ to $100$ to the $ATM$ of Banks.
- Population size is $100$, a three-digit number. Hence, the random numbers greater than $100$ will be ignored from the given random numbers.
- Random sample without replacement is to be obtained. Hence, repeated random numbers are ignored. Thus, the following random numbers are obtained :
$018, 096, 027, 007, 012, 054.$
- As the random sample of $5$ $ATM$ is to be obtained, we select first five random numbers from the random numbers above.
- Thus, the random sample of $5$ $ATM$ Is obtained as follows :
$018, 096, 027, 007, 012.$ View full question & answer→Question 183 Marks
State advantages of sampling.
AnswerThe advantages of sampling are as follows :
$(1)$ In sample study as few units are to be examined. detailed study can be done.
$(2)$ As few units are to be studied the survey work requires less time.
$(3)$ The cost of study is also very less.
$(4)$In sample study few persons are required for the survey work, hence experts can be appointed. This will Increase the reliability of the results.
$(5)$ In- certain survey special types of equipments are required. This is possible only if few units are to be studied.
$(6)$ When the test is of destructive nature, sampling is only the way out. In such cases population study is not possible.
$(7)$A large area is covered in the available time and money.
$(8)$ If proper method of sampling is employed. the results obtained will represent the population adequately.
View full question & answer→Question 193 Marks
Why is population inquiry usually not feasible in practice ?
Answer
- Sometimes even in situations where population inquiry can be undertaken, preference is given to sample inquiry because a population inquiry involves more time, money and man power. Moreover a large numbers of errors creep into the population inquiry due to the extensive and complicated task of organising population inquiry.
View full question & answer→Question 203 Marks
State the advantages of systematic random sampling.
AnswerThe advantages of systematic random sampling are as follows :
$(1)$ It is easier to draw a sample without mistakes as the order of the sample unit is automatically determined.
$(2)$ Sample is evenly spread over the population.
$(3)$ It requires less time and labour compared to simple random sampling and stratified random sampling.
View full question & answer→Question 213 Marks
Explain the meaning of population inquiry and sample inquiry with an illustration.
AnswerPopulation inquiry:
- The inquiry in which data are collected by inspecting all units of the population is called population inquiry.
Illustration:
- The population census conducted in our county for every ten years is population inquiry.
- In population census information is collected from each family of the country as well as from the members of the family. Hence. it is population inquiry.
Sample inquiry :
- The inquiry in which data are collected by inspecting units of a sample selected from the population is called sample inquiry.
Illustration :
- An inquiry regarding the annual income of some families selected randomly from the population of families residing in Ahmadabad city is the sample inquiry.
View full question & answer→Question 223 Marks
A systematic sample obtained from the population of $60$ persons Is as follows. $4, 14, 24, 34, 44, 54$
State the sample size and sampling interval.
View full question & answer→Question 233 Marks
To inquire about the health of $20$ children obtain all possible systematic samples of size $5$ children.
Answer$k=4$; Sample $1:1, 5, 9, 13, 17$
Sample $2:2, 6, 10, 14, 18$
Sample $3:3, 7, 11, 15, 19$
Sample $4:4, 8, 12, 16, 20$
View full question & answer→Question 243 Marks
To inquire about the quality of two products $A$ and $B$ produced in a factory, a $3 \%$ stratified random sample is drawn from the weekly production of $600$ units, in which $10$ units of product $A$ and $8$ units of product $B$ are consider. Use the following random numbers for selecting the units.
Random numbers for Product $A$: $3674, 0375, 2143, 5283, 7489, 1610, 8832, 5597, 2183, 0621, 2302, 3531, 9374, 2801, 7827$
Random numbers for Product $B$: $2911, 1483, 3648, 8588, 6002, 2426, 0967,6821, 1973, 4187, 7487, 1559, 8588, 6030, 4254$
[Hint: consider first three digits of random numbers]
AnswerProduct $A : 367, 037, 214, 528, 161, 559, 218, 062, 230, 353$
Product $B :291, 148, 364, 600, 242, 096, 197, 418$
View full question & answer→Question 253 Marks
To inquire about the daily Income of $40$ small traders and $20$ large traders of a city obtain stratified random sample of $10$ traders including $7$ small and $3$ large traders.
Random numbers for small traders: $13, 04, 65, 40, 76, 51, 29, 14, 36, 65, 99, 18, 82$
Random numbers for large traders: $03, 47, 86, 36, 61, 36, 28, 15, 10, 73, 96$
AnswerSmall traders: $13, 04, 40, 29, 14, 36, 18$; Large traders: $03, 36, 28$
View full question & answer→Question 263 Marks
From a population of $175$ units, to obtain a $4 %$ simple random sample without replacement use the following random numbers:
$160, 235, 715, 547, 1295, 197, 975, 358, 275, 108.$
AnswerThe random numbers obtained by dividing $175$ are:$160, 60, 15, 22, 70, 22, 100, 8, 100, 108.$
Sample units:$160, 60, 15, 22, 70, 22, 100.$
View full question & answer→Question 273 Marks
$15$ random numbers are as follows:
$62, 18, 09, 112, 85, 108, 75, 99, 29, 82, 30, 03, 36, 171, 203.$
Using these random numbers obtain a simple random sample of $5$ units without replacement from the population of $50$ units.
AnswerThe random numbers obtained by dividing $50$ are:$12, 18, 09, 12, 35, 08, 25, 49, 29, 32, 30, 03, 36, 21, 03.$
Sample units: $12, 18, 09, 35, 08.$
View full question & answer→Question 283 Marks
Use the following random numbers to obtain a simple random sample of $12$ students without replacement from $800$ students of a school to obtain the estimate of the average height of the students:
$938, 1260, 1044, 1138, 2028, 1800, 3044, 2510, 1620, 5742, 7338, 811, 4185, 1957, 5114.$
AnswerThe random numbers obtained by dividing $800$ are:$138, 460, 244, 338, 428, 200, 644, 110, 020, 142, 138, 011, 185, 357, 314$.
Sample units: $138, 460, 244, 338, 428, 200, 644, 110, 020, 142, 138, 011.$
View full question & answer→Question 293 Marks
There are $150$ factories in an industrial estate. Use the following random numbers to select a simple random sample of $6$ factories with replacement:
$274, 059, 008, 078, 115, 029, 115, 059, 169, 130.$
Answer$59, 8, 78, 115, 29, 115.$
View full question & answer→Question 303 Marks
Using the following random numbers, obtain a $2\%$ simple random sample with replacement from the population with $500$ units:
$1029, 2667, 9920, 3428, 0278, 1819, 3900, 0420, 1710, 2891, 5353, 6051, 0278, 1953, 1819.$
AnswerConsider the first three digits of given numbers: $102, 266, 342, 27, 181, 390, 42, 171, 289, 27.$
View full question & answer→Question 313 Marks
Using the following $15$ random numbers, obtain a simple random sample of size $10$ with replacement from the population of 200 units:
$053, 267, 156, 009, 119, 058, 011, 053, 196, 208, 200, 170, 301, 195, 278$.
Answer$53, 156, 9, 119, 58, 11, 53, 196, 200, 170.$
View full question & answer→Question 323 Marks
Use the following random numbers to select a simple random sample without replacement of $5%$ families of $160$ middle class families of an area to obtain the estimate of their economic standards:
$1537, 3370, 0264, 0721, 1940, 2016 1066, 1648, 2130, 0921, 2029, 0086, 0825, 0879, 3500.$
AnswerConsider the first three digits: $153, 26, 72,106, 92, 8, 82, 87.$
View full question & answer→Question 333 Marks
Use the following random numbers to select a simple random sample without replacement of $2%$ $TV$ sets of a lot of $300$ $TV$ sets to examine the quality of the $TV$ set:
$537, 239, 028, 329, 158, 220, 764, 486, 157, 194, 016, 135.$
Answer$239, 28, 158, 220, 157, 194.$
View full question & answer→Question 343 Marks
Ten random numbers of two digits are as follows:
$62, 35, 04, 61, 40, 89, 82, 18, 96, 21.$
Using these random numbers, select a simple random sample without replacement of $4$ units from a population having 50 units.
View full question & answer→Question 353 Marks
There are $500$ fields growing sugar cane. To determine the average yield of sugar cane per acre. Obtain a simple random sample without replacement of $10$ fields using the following random numbers:
$0375, I51, 4155, 3531, 1610, 5357, 1749, 5697, 0988, 2717, 5518, 3167, 0137, 3283, 1862, 0711, 2162, 4308, 1915, 0600.$
AnswerConsider the first three digits : $37, 145, 415, 353, 161, 174, 098, 271, 316, 013.$
View full question & answer→Question 363 Marks
To obtain the estimate of average weight of $1000$ students of a school, select a simple random sample without replacement of $15$ students using the following random numbers:
$0749, 1929, 0489, 0034, 5618, 0163, 0900, 1816, 0218, 1004, 0816, 0988, 1132, 0711, 0900, 1915, 0007, 8000, 4401, 0275, 0142, 2813, 0050, 0379, 0501.$
Answer$749, 489, 34, 163, 900, 218, 816, 988, 711, 7, 275, 142, 50, 379, 501.$
View full question & answer→Question 373 Marks
We have to obtain the information of monthly income of $1000$ workers of a factory by selecting $10$ workers from it. If the random number selected in the sampling interval is taken $67$, drawn systematic sample.
Answer$k= 100$ , Systematic sample : $67, 167, 267, 367, 467, 567. 667, 767, 867, 967$
View full question & answer→Question 383 Marks
To determine the average fare of $18$ taxis, obtain all possible systematic samples of $6$ taxis.
Answer$k = 3$, possible samples $3$
Sample $1: 1, 4, 7, 10, 13, 16 ,$ Sample $2:2, 5, 8, 11, 14, 17 ,$ Sample $3:3, 6, 9, 12, 15, 18$
View full question & answer→Question 393 Marks
A population has $300$ units. From this population a systematic sample of $10$ units is to be drawn. If the random number selected in the sampling interval is $18$, prepare the list of units of systematic sample.
Answer$k = 30$ , Systematic sample: $18, 48, 78, 108, 138, 168, 198, 228, 258, 288$
View full question & answer→Question 403 Marks
To test the quality of food served by $200$ restaurants of a city draw 10 % stratified random sample. From $200$ restaurants $140$ is large and $60$ are small. To draw the sample random numbers are as follows:
For large restaurant: $137, 408, 071, 191, 014, 120, 394, 222, 026, 090, 172, 304, 200, 215, 146, 013, 348, 113, 160, 181$
For small restaurant : $572, 089, 008, 328, 078, 432, 107, 138, 247, 078, 115, 209$
AnswerLarge restaurant: $137, 071, 191, 014,120, 026, 090, 172, 200,146 , 013, 113, 160, 181$
Small restaurant: $089, 008, 078, 107, 138, 115$
Stratified random sample: $137, 071, 191, 014, 120, 026, 090, 172, 200, 146, 013, 113, 160, 181, 089, 008,078, 107, 138, 115$
View full question & answer→Question 413 Marks
To inquire regarding the discipline of $60$ students of Std. $XII$ draw simple random sample with replacement of $10$ students. The random numbers are as follows:
$34, 65, 60, 97, 46, 86, 03, 47, 41, 34, 07, 87, 18, 49, 73$
Answer$34, 60, 46, 03, 47, 41, 34, 07, 18, 49$
View full question & answer→Question 423 Marks
Using the following random numbers draw simple random sample without replacement of size $3 \%$ from the population of size $300$ units:
$3674, 0375, 2143, 5283, 7489, 1610, 2183, 5597, 0621, 2302, 3531, 2801, 7827, 0715, 3005:$
Answer$037, 214, 161, 218, 062, 230, 280, 071, 300$
View full question & answer→