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Application

?1. Choose the best sampling method to obtain the individuals in the sample for each problem. Explain how you would perform the sampling method you have chosen.

a. The province of Quezon is considering the construction of a new LRT line. The province wants to

conduct a survey to ask the residents if they agree to use thier taxes for this purpose.

b. A school official wants to know the students' opinions regarding the student services offered by the

school.

c. A reporter wants to know the opinion of the people of the Philippines about waging a war against Wakanda because of territorial disputes.

2. Determine whether the underlined value is a parameter or a statistics.

a. According to a national survey on cigarette addiction. 10% pf respondents smoke at least 5 cigarettes a day within the past 3 months.

b. A study of 6,076 adults who use public toilets in Metro Manila found that 12% of then did not wash

their hands before leaving the toilet.

C. An interview conducted with 100 females that are at least 20 years old in Metro Manila reveals that

20% of them know the minimum age requirement for a presidential candidate.

LESSON 10: RANDOM SAMPLING LET'S DEVELOP As stated in the introduction, it is difcult, or sometimes impossible, for the researchers to gather data om the entire population. As a recourse, researchers gather data from a small part of the population called sample. This sample is selected li'om the population and the data gathered from it will represent the data that can be gathered from the entire population. The process of selecting samples is called sampling method Sampling method is concerned with the selection of a subset of population that will be used to estimate the characteristics of the entire population. Researchers nd it practical because the cost is lower, the data collection is faster, and the accuracy and quality of data can be improved easily. Explore 10.1 RANDOM SAMPLING A sample survey will be conducted to estimate the value of some characteristics of the population. The inferences about the population depend on how the samples are being selected. That is why the selection or the sampling method that will be utilized in any research process must be appropriate. Random sampling is one of the methods of choosing the samples that will be used in the sample survey. Random sampling is a method wherein each element of the population has an equal chance of being chosen to represent the population. If the researcher used random sampling, it is guaranteed that the sample selected is a true representative of the population. This also ensures that the inferences about the population are also valid and reliable. 10.2 TYPES OF RANDOM SAMPLING There are 5 main types of random sampling: (1) simple random sampling, (2) systematic sampling, (3) stratied sampling, (4) cluster sampling. (5) multi-stage sampling. The researchers can use any of the random sampling methods in selecting the respondents for their study. Take note that the best method of selecting the samples from the population is by choosing the appropriate one. 10.2.1 SIMPLE RANDOM SAMPLING Simple random sampling is the simplest form of random sampling where each element or member of the population has an equal chance of being included in the sample. The most commonly used is the lottery method. A number is assigned to every element of the population. Each number is written on a small piece of paper. Each paper is rolled and put in a bowl or box, then the researcher will pick from it. If the researcher needs 250 respondents, then he will pick 250 pieces of paper from the bowl or box. Using simple random sampling is idea] when the population is small. It is a fair method of selecting the respondents because each member has an equal chance to be chosen and the researcher is sure that the sample is a good representative of the population. It is important that the selected sample is a true representative of the population so that the inferences that will be drawn from that sample is a good estimate of it. However, simple random sampling requires the complete list of names of all the member in the population. Researchers may also use a computer-aided selection of samples or the table of random numbers if dealing with a large population. 10.2.2 SYSTEMATIC SAMPLING Systematic sampling is another type of random sampling which is also known as the interval sampling. This method considers an interval in selecting a sample from a given population. First, assign a number to each member of the population from 1 to N (Where N is the total number of population) and decide the sample size (n) that you need to consider in your study. The interval size (It) is determined using the formula: k : N/'n always round off the interval to the nearest whole number. Example: There are LOCI) students in the population and we need to consider a sample size of 250. Find the intervals size (k).\\ Solution: k : N/'n = 1.0001'250 = 4 Answer: The interval is 4. Choose a number from 1 to 4, example number 4. Gabuyo, Y. et.al., (2016). Statistics and Probability. Paligsahan, Quezon City. 91 Hence, the 4" name will be the first sample. The second sample is the 8" name. The 12" name will be the third sample ans so on. face are selected samples. Continue this process until the 250" sample is determined. The example is illustrated on the table below, wherein the numbers in Bold is determined. The example is illustrated on the table below, wherein tic face are the selected samples. 21 41 61 81 101 121 141 161 18 201 891 2 22 42 62 82 102 122 142 162 182 202 . . . 892 3 23 43 63 83 103 123 143 163 183 203 . . . 892 4 24 44 64 84 104 124 144 164 184 204 . .. 894 5 25 45 65 85 105 125 145 65 185 205 895 6 26 46 66 86 106 126 146 166 186 206 . . . 896 27 47 67 87 107 127 147 167 187 207 897 8 28 48 68 88 108 128 148 168 188 208 . . . 898 29 49 69 89 109 129 149 169 189 209 899 10 30 50 70 90 110 130 150 170 190 210 . . . 900 1 1 31 5 71 91 111 131 151 171 191 21 . . . 991 12 32 52 72 92 112 132 152 172 192 212 . . . 992 13 33 53 73 93 113 133 153 173 193 213 . . . 992 14 34 54 74 94 114 134 154 174 194 214 . .. 994 15 35 55 75 95 115 135 155 175 195 215 995 16 36 56 76 96 116 136 156 176 196 216 996 17 37 57 77 97 17 137 157 177 197 217 997 18 38 58 78 98 118 138 158 178 198 218 98 19 39 59 79 99 119 139 159 179 199 219 999 20 40 60 80 100 120 140 160 180 200 220 1000 . .. Gabuyo, Y. et.al., (2016). Statistics and Probability. Paligsahan, Quezon City. 9292 10.2.3 STRATIFIED SAMPLING Stratified sampling is a random sampling method that divides a population into different homogeneous subgroups called strata. Random samples will be selected from each stratum so that the population will be well represented. WE use stratified random sampling when we consider subgroups like year level of students, gender, and age among others. There are two types of stratified random sampling - simple stratified sampling and proportional stratified sampling, Simple stratified sampling is used when the population is divided into strata with common characteristic/s and if we decide to get an equal number of samples from each stratum. Example 1: Out of 1,000 students in a certain university, use the simple stratified sampling method to get a sample size of 200. Solution: Using the simple stratified sampling, strata will be determined according to grade level and the sample size from each grade level will be 50. Grade Level Enrolled Students (N=1,000) Sample size (n=200) Grade 7 350 50 Grade 8 250 50 Grade 9 225 50 Grade 10 175 50 Answer: 50 students from each grade level will be selected as the sample. The second type of stratified random sampling is proportional stratified sampling. In this method, the sample size is proportional to the number of the members of the stratum. This means that the smaller the number of the members of the stratum, the smaller the sample size from that stratum will be. Example 2: Out of 1,000 students in a certain university, use the proportional stratified sampling method to get a sample size of 200 Solution: Using the proportional stratified sampling, the strata will be determined according to grade level and the sample size form a stratum will depend on the number of students that belong to that stratum Grade Level Enrolled Students (N=1,000) Proportion Sample Size (n=200) Grade 7 350 35% 70 Grade 8 250 25% 50 Grade 9 225 22.5% 45 Grade 10 175 17.5% 35 Answer: Since 35% of the enrolled students are Grade 7, 35% of the sample must be Grade 7 students. 35% of 200 is 70. Hence 70, Grade 7 students must be selected to represent the population. Meanwhile, Grade 8, 9, and 10 are 50, 45 and 35 students respectively. 10.2.4 CLUSTER SAMPLING The fourth type of random sampling is cluster sampling. This type of random sampling is also called area sampling because it is usually used on a geographical basis. Cluster sampling requires a complete list of clusters that represent the sampling frame. Choose a few clusters randomly as a source of primary data and the data that can be collected from each cluster to represent the characteristics of the whole population. th cluster to represent the characteristics of the wh 12 9 10 11 12 Sample Cluster Population (2 cluster) gram above illustrates the cluster sampling method. Fr clusters 5, 6, 11, and 12 can be selected to represent the 12 d collected randomly from four clustere using either Gabuyo, Y. et.al., (2016). Statistics and Probability. Paligsahan, Quezon City. 9393 The diagram above illustrates the cluster sampling method. From the cluster population. clusters 5,6,1! and 12 can be selected represent the 12 clusters. Primary data will be collected randomly from four clustered samples using either simple random sampling or systematic sampling. 10.2.5 Mum-STAGE SAMPLING The last type of random sampling is the multi-stage sampling. It involves two or more stages in selecting the samples from a given population. Multi-stage sanpling also reduces the sample preparation cost because it may require only the last stage of choosing the samples. but the accuracy is lower because of the sampling error. 10.3 PARAMETERS AND STATISTICS The min objective of conducting a survey is to estimate the value of some of the characteristics of a population. Let us consider one of the results of XYZ survey before the May 2022 presidential election. The actual percentages of all the voters represent the population parameter. while the estimate of those percentages based from the sample is known as the sample statistic. The sampling method used in selecting the sample data strongly affects the qual'ay of the sample statistics with regards to its representatives and accuracy. The table below shows a list of the common symbols used for parameter and statistics: Population mean p Sample Mean 1? Population standard deviation 0' Sample standard deviation (8) Population Variance ([2 Sample variance (52) Population proportion (P) Sample proportion t3