Extracted text: Activity 1.2 Suppose that a population consists of the six (6) employees in a small business The random variable of interest x, is the number of years the employee has been wih the business. The values of the variable are as follows: Lesson Sampling Distributions WN you select a random sample from a population, the numerical descriptive measures you calculate from the sample are called statistics. These statistics vary or change from each different random sample you select, that is, they are random variables. The probability distributions for statistics are called sampling distributions. Years in the Business 1 Employees Activity 1.1 Suppose that a population consists of the six (6) employees in a small business. The random variable of interest x, is the number of years the employee has been with the business. The values of the variable are as follows: Shiela 2 Claudine page2 3 Mildred Employees Years in the Business 4 Divine Shiela 5 Bridgette i page1 Claudine 3 Sophia Mildred Divine What is the sampling distribution of the saạmple means for a sample of sıze 27 Steps in Constructing a Sample Distribution Bridgette 1. Find the number of possible samples that can be drawn from the finte population using combination formula. Sophia What is the population mean, population variance and population standard deviation of the given data? NCn= Solution: Given the vales of x = 1,2,3.4,5,6. We first solve for the population mean, we get 2. Randomly draw all possible sample of sıze n from a iscrete, hnite population of size N. Then we solve for the population variance and standard deviation Employees | Shiela Claudine Mildred 3. List observed values of the statistic and its corresponding trequency of occurrence Solution to Activity 12 To generate the sampling distribulion of the sample means we need to collect all possible sample sıze without replacement from the population Year in the Business (x) X-p -2.5 -1.5 -0.5 (x-p) 6 25 2.25 3 0.25 Divine Bridgette Sophia Step 1. possible samples of size 2 Note that N=6 and n=2 4. 0.5 0.25 By applying the combination formula, we can determine the number of 1.5 2.5 2.25 6.25 6. 6C2 =-" 2"= 15 Total 21 17.50 (-u. 17.5e There are 15 possible samples of size 2. " = 2.92 r-u. - 292 = 1.71 17.50 The population mean is 3.5, the population variance is 2.92, and the population standard deviation is 1.71. Step 2. the population. Now we list the 15 distinct samples of size 2 which can be drawn from Table 1: A Possible Samples of Size 2 Observations Years 1,2 1,3 1,4 Employees Shiela, Claudine Shiela, Mildred Shiela, Divine Shiela, Bridgette Shiela, Sophia Claudine, Milded Claudine, Divine Claudine. Bridgette Claudine. Sophia Mildred. Divine Mildred, Bridgette Mildred. Sophia Divine. Bridgette Divine. Sophia Bridgette, Sophia page3 3 4 1,5 1,6 2,3 2,4 2,5 2,6 3,4 3,5 3,6 4,5 4,6 5.6 7 8 6. 10 11 12 13 14 answer the ff: 15 The table shows the sampling distribution of the population consists of six (6) employees in a small business of sample means for the sample of size 2. There are four newly hired salespersons at Honda Cars Taguig Branch. The number of motorcycles sold by each newly hired salesperson last month is 4.5, 8, and9. a. Complete the information needed in the table below. b. How many samples of size 2 are possible? c. List all possible samples of size 2. Observation Sample