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xnun lo Joothe a'golf mine In conducting a research the number of possible samples of size n that can be drawn from the population of size N is C(N,n) where C(N,n)= n ! (N-n)in! Where Nain1848084 aNA aSITZITATE posidue The sample means obtained will form a frequency distribution and the corresponding probability distribution can be constructed. This distribution is called the sampling distribution of the sample means. The sampling distribution of the sample means is the frequency distribution of the sample means taken from the population. :25181 ovicufonil The histogram of the sampling distribution of the sample means is a bar graph constructed by plotting the sample means along the horizontal axis and the probabilities along the vertical axis.binbusta Inoino) anowudreib gnilamsa bris gailqmise sidefive viqqs side ai nominal ofT ispollib ni emeldon stil-losT svloe of asom slams? sri to basbrist2 sonamnotiog Sampling Distribution of the Sample Means 2 mobnisi zoisuzulil 109wted eordainunipic grimss I foilnoeall 120M A population consist of the numbers 2,4,5,9 and 10, Let us list all possible sample of size 3 from this population and compute the mean of each sample. gridniNT booth? Sample Mean (2+4+9)/3= 5.00 2,4, 10 5.33 2suisV 970) 2,4,5 3.67 2,9,10 7.00 2,9,5 5.3 2, 10,5 5.67 1 1 4,9,10 7.67 4,9,5 6.00 4,10.5 6.33 In 9 9,10,5 guilqinse mobnisi estelleulli \\ There are 10 possible samples of size of 3 that can be drawn from the given population. *** The number of sample size n that can be drawn from a population of size N is given by NCn. pilausie ban istomsing noowned 29demandaid This time, let us make the frequency distribution of the sample means. We shall call this frequency distribution, the sampling distribution of the sample means. .".un wary will www bybig ad sabol'l) 230Madden .TH 091/450 POL. 71 Sample Mean PITTed |OfFrequency 1/ 1/07 en2 :bomn A 3.67 5.00 1 5.33 2 5.67 1 6.00 92019279 6.33 7.00 1 7.67 1 8.00 1 TotalA sampling distribution of the sample means is a frequency distribution using the means computed from all possible random samples of a specific size taken from the population. Observe that the means vary from sample to sample, thus any mean based on the sample drawn from a population is expected to assume different value for the samples, So this leads us to a conclusion that a sample mean is a random variable, which depends on a particular sample, Being a random variable, it has a probability distribution of the sample means also called the sampling distribution of the sample mean colqraszs brosse wo mon] Table 3.1: Sampling Distribution of the Sample Means Ruq zill rot .nom notslugon A motowns' Sample Mean ( X ) Frequency Probability P(X ) 3.67 -=0.10 10 5.00 1 *=0.10 10 5.33 2 2=0.20 10 5.67 1 1=0.10 10 6.00 1 1=0.10 10 6.33 1 1=0.10 10 7.00 DIS wolsa 10 bluow nonci 7.67 1 noilslug 1=0.10 10 bigis asom 8.00 | blow oilalist A lio 91 ni agob is to my -=0.10 9mi Sri 9d ob Total n=10 1.00 W ortailsle A mioinge foordbe dgiri lis to zogmovs intoq sbang to notsivsb bisbaste ords ai mouslugoq Observe that the means of the samples are less than or greater than the mean of the population. The difference between the sample mean and the population mean is called the sampling error. It is due to sampling. 101 hogque to level sdi enimmoish of nerw sW notluluferioo ointe oils syrusdo ibili alston voll to noislugoq ord to nothoqoIq ord ai ,5260 aids ni astorusing A svisitin To olqmise s To noihogonq gnibnogasnoo sri zi offerste bolster A ovitshini tolled ath hogque Your Understanding englov visit DAY3 & 4: problems POPULATION, PARAMETER, SAMPLE, STATISTIC A population includes all of the elements from a set of data. A sample consists one or more observations drawn from the population. What Is a Parameter? It is a measure of a characteristic of an entire population (a mass of all units under consideration that share common characteristics) based on all the elements within that population. For example, all people living in one city, all-male teenagers in the world, all elements in a shopping trolley, or all students in a classroom. If you ask all employees in a factory what kind of lunch they prefer and half of them say pasta, you get a parameter here - 50% of the employees like pasta for lunch. On the other hand, it's impossible to count how many men in the whole world like pasta for lunch, since you can't ask all of them about their choice. In that case, you'd probably survey just a representative sample (a portion) of them and extrapolate the answer to the entire population of men. This brings us to the other measure called statistic. It's a measure of characteristic saying something about a fraction (a sample) of the population under study. A sample in statistics is a part or portion of a population. The goal is to estimate a certain population parameter. You can draw multiple samples from a given population, and the statistic (the result) acquired from different samples will vary, depending on the samples. So, using data about asample or portion allows you to estimate the characteristics of an entire population. A parameter is a number that describes a population. A statistic is a number that we calculate from a sample. guilqin A From our first example: Parameter: A population proportion. For this population of students at a small college, 0.60 are eligible for financial aid. vns euids Statistics: Sample proportions that vary. In the example, 0.75, 0.625, and 0.375 are all statistics It , that describe the proportion eligible for financial aid in a sample of 8 students. 7 5 21 nom ofqmine Iqmse offs bellso oals aniss olqmine ordi to nobudnaib vildedong s and From our second example: Parameter: A population mean. For this population of students at a small college, the mean amount of financial aid is $1,500. Statistics: Sample means that vary. In the example, $2,087.50, $1,325.00, and $687.50 are all statistics that describe the mean amount of financial aid received by a sample of 8 students. 01.0= 00.2 OS.0=- EE.a 01.0=- ca.a 00.8 Examples of Parameters and Statistics EE. Below are some more example of parameters and statistics: 00.T Suppose we study the population of dogs in Kansas City. A parameter of this population would be the mean height of all dogs in the city. A statistic would be the mean height of 50 of these dogs. We will consider a study of high school seniors in the United States. A parameter of this population is the standard deviation of grade point averages of all high school seniors. A statistic is the standard deviation of the grade point averages of a sample of 1000 high school seniors. JO We consider all of the likely voters for an upcoming election, There will be a ballot initiative to change the state constitution. We wish to determine the level of support for this ballot initiative. A parameter, in this case, is the proportion of the population of likely voters that support the ballot initiative. A related statistic is the corresponding proportion of a sample of likely voters. from 10 ono alatenoo siquine A wish to move s mont albanists ord to lis abulom noitaluquq A nouslugoq oin med numb moodnondo signsq lle sigmars 101 nobalugog band aidhew aimsmets and is no beexd ropebabesdo nomammo siden SANI O Boy blood I vidw musiqzs boy tigint woll "forland of n nisles Bor bluow word ACTIVITY 1: DRAWING CARDS Jingog oth To wdmom visy gnizovine and Tothe iqme? Samples of three cards are drawn at random from a population of eight cards numbered 1-8. isfuqmoo s nwa.b How many possible samples can be drawn? oniqiliT EEI 10 voyme A .s b. Construct the sampling distribution of the sample means :nonulo' 'ACTIVITY 2:01 10 085 ishi bauol moblido loordoa visiomels adds to YouTu2 1939T A d .sasdo es berlieeslo ed How many different samples of size n=3 can be selected from a population with the following sizes? a. N=4 aww bonsq work. Neg w lIsm ords ganghas nozing dixie visvo to idglew ogslovs oT .. C. N=20 .di all d. N=50 e. N=30 ACTIVITY 3: Deepen Your Understanding Solve the following problems 1. Random samples of size n=2 are drawn from a finite population consisting of the numbers 5,6,7,8 and 9. a. How many possible samples are there? b. List all the possible samples and the corresponding mean for each sample. c. Construct the sampling distribution of the sample means ACTIVITY 4: For each statement, identify whether the number underlined are statistics or parameter. a. Of all Filipino Kindergarten teachers, 32% say that knowing the alphabet is an essential skill . b. Of the 800 Filipino Kindergarten teachers polled, 34% say that knowing the alphabet is an essential skill. 1. Of the US adult population, 36% has an allergy. A sample of 1200 randomly selected adults resulted in 33.2% reporting an allergy.a. Who is the population? ! ! b. What is the sample? " c. Identify the statistic and give its value. d. Identify the parameter and give its value. 2. In your own words, explain why the parameter is fixed and the statistic varies. 3. Select 90 students currently enrolled at NCSU and ask how many years they've attended the university, how old are they and if they live on campus. a. What is the population? b. What is the sample? 4. Suppose a 12-year-old asked you to explain the difference between a sample and population, how would you explain it to him/her? How might you explain why would you want to take a sample rather than surveying very member of the population. 5. Identify the population and sample a. A survey of 1353 Filipino households found that 18% of the households own a computer. Population: Sample: b. A recent survey of 2625 elementary school children found that 28% of the children could be classified as obese. Population: Sample: .! ! c. The average weight of every sixth person entering the mall within a 3-hour period was 146 1b. Population: Sample