PLEASE HELP ME TO ANSWER THEM ALL CORRECTLY FOR AN UPVOTE AND POSITIVE RATINGS. THANK you

Below are the references:)

2| Page Step 2: Since k = 3 0 and the starting point given is 3, the sample of selected students are: 1st student: 3rd Lesson 9 Random Sampling 6th student: 123 + 30 = 153rd 2nd student: 3+30 = 33rd 7th student 153 + 30 = 183rd 3rd student: 33+30 = 63rd at student: 183 + 30 = 213rd 4th student: 63+30 = 93rd 9th student 213 + 30 = 243rd Background Information th student: 93+30 = 123rd 10th student: 243 + 30 = 273rd A consumer is interested in buying grapes. Before deciding, the consumer requests a piece from the bunch of grapes shown by the seller. Based upon this piece, the consumer decided to buy . Stratified random sampling the bunch of grapes. A sampling procedure wherein the members of the population are grouped based on their The consumer's decision to buy the grapes was based only on a piece, or sample, of the homogeneity. This technique is used when there are a number of distinct subgroups in the bunch. Obviously, it was not needed for the consumer to buy and eat the whole bunch of grapes population, within each of which is required that there is full representation. The sample is before determining whether these grapes tasted good enough to purchase. This idea of selecting a constructed by classifying the population into subpopulations or strata, based on some portion, or sample, to determine the taste or characteristics of all the grapes, or population, is the characteristics of the population such as age, gender, or socio-economic status. The selection of concept of sampling. elements is then made separately from within each stratum, usually by random or systematic sampling methods. DEFINITION Example. Using stratified random sampling, select a sample of 387 students from the population which are grouped according to the cities they come from. The table below shows the number of students A population refers to the entire group that is under study or investigation. per city. A sample is a subset taken from a population, either by random or non-random sampling techniques. City Population ( N) A sample is a representation of the population where one hopes to draw valid conclusions from about A 13 000 the population. B 10 500 8 000 Sampling is the process of selecting a portion, or sample, of the entire population. D 5 000 A simple random sampling or random sampling is a selection of elements derived from a population Total 36 500 which is the subject of the investigation or experiment, where each sample point has an equal chance of being selected using the appropriate sampling technique. Solution. To determine the number of students to be taken as sample from each City, divide the number of students per city (stratum) by the total population (which is 36 500) and multiply the result by the total sample size Types of Random Sampling Techniques (which is 387) 1. Lottery sampling A sampling technique where every member of the population has an equal chance of City Population ( N) Solution Sample (n) being selected. The procedure is carried out by randomly picking numbers, with each 13 000 number corresponds to each member of the population. 13 000 36 500 (387) = 137.83 138 Example. Drawing of winning prizes from the tambiolo. 10 500 10 500 36 500 (387) =111.33 111 2. Systematic sampling A sampling technique in which members of the population are ordered in some way 8 000 C 8 000 35 such as alphabetically or numerically and samples are selected in intervals called 36 500 (387) = 84.82 sample intervals. In this technique, a starting point is randomly selected from the first 5 000 k positions, and then, every kth number, is selected from the sample. Since & is the 5 000 36 500 (387) =53.01 53 ratio of the population size to sample size, to find the k use the formula: L _ Population size Total 36 500 387 samplesize Example. A Science teacher decides to select a sample of 10 students from Based on the table, 138students will be drawn from City A, 111 students from City B, 85 students her large lecture class containing 300 students to be part of an from City C, and 53 students from D. The selection of students from each City may use random or experiment using the systematic sampling procedure. If each systematic sampling methods. student has an assigned number from 1 to 300 and she randomly selects 3 as her starting point, identify the students selected for the 4. Cluster sampling experiment. It is sometimes called area sampling, the population is divided into groups or clusters, usually Solution. based upon geographic location, and these clusters contain data values which are heterogenous. A Step 1: Identify the value of . simple random sample of clusters is selected to represent the population. Ideally, the clusters should be similar and be a representative small-scale version of the overall population population 300 Example. A statistician wants to determine the number of children per family in Victoria. 10 sample size To minimize the cost of selecting a sample, the statistician decides to divide the Victoria into k = 30 Barangays (clusters) and use the cluster sampling procedure to select the sample. A random sample of the Barangays are selected and every family on the Barangay are interviewed to determine the number of children in the family.5. Multi-stage sampling Illustrative Example 1 It is done using a combination of different sampling techniques. Lesson 10 Statistic vs Parameter Construct a sampling distribution of the mean and a histogram for the set of data below. Example. When selecting respondents for a national election survey, lottery method may be used 86 89 92 95 98 to select regions and cities. Then, utilize stratified sampling to determine the number of respondents from the chosen areas and clusters. In most applications of Statistics, researchers use a sample rather than the entire population Solution. since it is usually impractical or impossible to obtain all the population observations or measurements; Step 1. Solve for the population mean. DEFINITION thus, sample information are used to estimate the characteristics of a population. That is, the use of a statistic to make inferences about the corresponding population parameter is being done. 86+89+92+95+98 = 92 A nonrandom sampling is used when the sample is not a proportion of the population and DEFINITION when there is no system in selecting a sample. This is often used by the researchers to elicit and gather quick responses for questions which do not require confidentiality. The researcher A statistic is a number which describes a characteristic of a sample. It can be directly Step 2. Construct all random samples consisting of three observation ( n = 3) from states prejudice in the choice of the sample giving the members of the population unequal computed and observed. It serves as estimator of the population parameter. the given data set. Arrange the observations in ascending order without chances to be selected. replacement and repetition. Then get the sample mean of each random A parameter is a number which describes a characteristic of a population. While statistic can sample. See the table below. be directly computed and observed, the value of a parameter can be approximated and is not necessarily equal to the statistic of a sample. Sample Computation: Types of Nonrandom Sampling Techniques 2x 86489492 - 89 1. Quota sampling 3 The researcher limits the number of his samples based on the required number of the The following are examples of statistic and parameter. subject under investigation. The population is first segmented into mutually exclusive Statistic Parameter Random Sample ( n = 3) ample Mean (x) subgroups, then judgement used to select subjects or units from each segment is sample mean population mean 86, 89, 92 89 based on the specified proportion. For example, an interviewer may be told to sample 200 females and 300 males sample standard deviation population standard deviation 86, 89, 95 90 sample variance population variance $6, 89, 98 91 between age 45 and 60. 86, 92, 95 91 Mean screen time of 1000 Grade 11 Mean screen time of all Grade 11 92 2. Convenience sampling students in Tarlac students in Tarlac 86, 92, 98 The researcher conducts a study at his convenient time, preferred place, or venue. It 86, 95, 98 93 Standard deviation of weights of Standard deviation of weights of all is the most convenient and fastest sampling technique that make use of telephone, watermelons from one farm. watermelons in the region. 89, 92, 95 92 mobile phones, or the internet. It simply uses results that are readily available 89, 92, 98 93 89, 95, 98 94 3. Purposive sampling In calculating a statistic, such as a sample mean, from a random sample of the population, the 95 computed statistic is not necessarily equal to the population parameter. Furthermore, taking another 2, 95, 98 It is used in very small sample sizes. Choosing samples is based on a certain criteria and rules laid down by the researcher. random sample from the same population may result to a different computed statistic. But both are Based on the table, there are ten (10) random samples which lead to ten (10) sample means. Observe For example, this can be used if the sample of the study are deans of universities or estimates of the parameter. This clearly shows that the statistics which can be computed from a area managers of certain institutions. randomly selected sample of the given population are distinct. If so, what could be the distribution of that the sample mean 89, 90, 94, and 95 appeared only once; thus, their probability is values that can be computed for the statistics? What is the frequency with which different values for P(X)= 1/10 or 0.1 the statistic will be computed to estimate the parameter? Since the different random sampling techniques were presented, the next thing to be Since the sample mean 91, 92, and 93 appeared twice, their probability is determined is the sample size. P(X) = 2/10 or 0.2 The sample size n is determined by the formula N Lesson 11 Sampling Distribution of Statistics n = 1 + Ne2 Step 3. Construct the sampling distribution of the sample means. where: N - is the population size; and Sample Mean (X) Probability e - is the margin of error In this section, sampling distribution will be discussed which is used to represent the estimates 89 0.1 of the population parameter. 90 0.1 This formula is known as Slovin's Formula. DEFINITION 91 0.2 92 0.2 Illustrative Example A sampling distribution is the probability distribution when all possible samples of size are A researcher wants to study the academic performance in Mathematics of students in a certain 93 0.2 repeatedly drawn from a population. school. The school has a population of 12 000 students. If the researcher allows a margin of error of 5%, 94 0.1 how many students must he include in his sample? 95 The sample size is computed as follows: 0. 1 Solution. Given: / = 12 000 N e= 5% or 0.05 " 1+ Nez Observe that the total probability of all the sample means must be equal to 1. 12 000 1+12 000(0.05)2 12 000 1+12 000(0.0025) Step 4. Construct the histogram of the sample means. 12 000 1430 12 00 n = 387.096 # 387 Thus, the researcher must take 387 students as his sampleActivity Sheet # 5 WRITTEN WORK # 5 A. Let's Sample! Direction: Determine if the following situations use random or non-random sampling. Then, identify what type of random or non-random sampling technique was used. Sample Answer: Random - Stratified 1. Every tenth person boarding a plane is searched thoroughly. 2. There are 30 freshmen, 20 sophomores, 10 juniors, and 5 seniors enrolled in a certain course. Samples are to be taken from their total number of students per year level. 3. Minority group of senators are to be interviewed. 4. Every five files out of 500 files will be chosen. 5. Animals going astray are to be observed. 6. Two thousand respondents nationwide, from regions down to Barangays are selected for national election survey. 7. Five hundred "likes" in Facebook are used as basis for making A decision. 8. Selected respondents for a study are those with Acquired Immune Deficiency Syndrome (AIDS). 9. Ten names of students were picked out from a box containing 1000 names written in rolled paper. 10. Respondents are chosen from a list in the telephone directory. Every 11th name was picked.Every Thin name was picked. B. Draw a Sample! Direction: Identify the sample size for each of the following problems. Show your complete solution. 1. How many samples must I pick from 800 members of Mathematics Club (a) if a margin of error of 10% is used? (b) if margin of error 5% is used? (c) how about 1%? 2. There are 10,000 sacks of rice. How many sacks of rice must be distributed to Town A, B, and C if Town has 15,000 families, Town B has 12,000 families, Town C has 7,000? PERFORMANCE TASK # 5 Problem: Find the mean of the set of data below and construct a sampling distribution, without replacement and repetition, by selecting 5 samples at a time ( = 5). Construct a histogram of the sample means. 5 8 11 14 17 20 23 Scoring Rubric for Activities 2 and 4 Scoring Rubric for Activity 4 (Histogram) (Solving) Description Score Description Score All steps are done correctly. The answer Graph is precise, neat and legible. Axes are labeled accurately. 5 5 is correct and is labeled accurately The graph is labeled with the correct title Few steps are done incorrectly. Graph is precise, neat and legible. Axes are not labeled accurately. The answer is correct and is labeled The graph is labeled with the correct title. accurately. Correct answer and is labeled Graph is mostly precise, neat and legible. Axes are not labeled 3 3 accurately with missing steps. accurately. The graph is labeled with the incorrect title Incorrect answer and was not labeled Graph is mostly precise, neat and legible. Axes are not labeled, with partially correct steps 2 and no title was written. Incorrect answer because the work is Graph is imprecise, messy and illegible. Axes are not labeled, and 1 incorrect from the first step. no title was written. No answer was written 0 No graph was drawn. 0