Statistics and probab

ole group br reeds not to method en as sa wants to use the Table of Random Numbers in determining the students that In + should be in his sample. enc 4. For your research on culture, you interviewed people from each province in the Cordillera Administrative Region. 5. A Statistics student did a research on effects of watching math lessons on social media. He randomly selected two grade levels in a small Junior High School and interviewed each of the students in those grade levels.14. What is the probability that the sample mean lies above 515? a. 3.01% c. 46.99% b. 23.50% d. 96.99% 15. What is the probability that the sample mean lies below 498? a. 4.94% c. 40.13% b. 9.87% d. 59.87%What I Know This pre-test will determine your prior knowledge of the topic. If you are able to answer all the test items correctly, then you may skip studying this learning material and proceed to the next learning module. Direction: Choose the letter of the correct answer and write it on each blank provided. Use capital letters. 1. This is a type of random sampling in which a list of elements is used as a sampling frame and the elements to be included in the sample are chosen by skipping through the list at a regular interval. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 2. This is a type of sampling technique where lottery method or Table of Random Numbers can be used to select the elements of the sample. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 3. This is a type of random sampling technique in which the population is first divided into strata and then the samples are obtained by randomly selecting them from each stratum. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 4. This type of random sampling method is done by dividing first the entire population into small groups, then some of the groups are randomly selected. The samples from the randomly selected groups are then analyzed. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 5. This is a characteristic that describes the sample. A. statistic B. parameter C. sample D. population 6. It pertains to the characteristic that describes the population. A. parameter B. population C. sample D. statistic 7. This is a term in Statistics which pertains to the subgroup of a population. A. parameter B. population C. sample D. statistic 8. Which of the following is an example of a statistic? A. x B. o C. 62 D. Har 9. Which of the following is an example of a parameter? A. Among the 50 front liners in the general hospital, only 10 were randomly chosen to be vaccinated . B. In a sample of 1,500 senior high school students, 5% of them are part- time workers . C. The teacher randomly selected 5 students to recite in Math. D. The Philippines consists of 7, 107 islands. For #10-13, refer to this given population (5, 6, 10) 10. What is the population mean in the given data above? A. 21 B. 7 C. 4.67 D. 2.16 11. What is the population variance of the data? A. 21 B. 7 C. 4.67 D. 2.16 12. Find the population standard deviation of the data set. A. 21 B. 7 C. 4.67 D. 2.16 13. Compute the mean uz of a sampling distribution of means of the data set. A. 21 B. 7 C. 4.67 D. 2.16 14. If the population variance of a data set is 11. 09, what is its population standard deviation? A. 22.18 B. 11.09 C. 6.67 D. 3.33 15. Find the ux of a sampling distribution of means of a sample consisting of values 4, 4, 8. A. 5.33 B. 10.66 C. 15.33 D. 20.31What's More Activity 1: Examine the given population below and decide which among the identified sampling techniques is best suited: simple random sampling, systematics random sampling, stratified random sampling, or cluster random sampling. Write your answer on the blank provided. 1. You were given a list of 100 Grade 11 students for your experiment. You selected every 5" name on the list. 2. In a survey conducted in your school, the subjects of the survey were selected by using the Table of Random Numbers. 3. Mr. Santos wants to make a study on the effects of distance learning in this time of pandemic among 2, 500 Senior High School students in his town. He 14Assessment This assessment aims to measure how much you have learned from this module. Read and understand each statement before choosing the correct answer. Write your answer on the space provided. 1. This is a type of random sampling technique in which the population is first divided into strata and then the samples are obtained by randomly selecting them from each stratum. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 2. This is a type of sampling technique where lottery method or Table of Random Numbers can be used to select the elements of the sample. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 3. This is a type of random sampling in which a list of elements is used as a sampling frame and the elements to be included in the sample are chosen by skipping through the list at a regular interval. A. simple random sampling C. stratified random sampling B. systematic random sampling D. cluster random sampling 4. This type of random sampling method is done by dividing first the entire population into small groups, then some of the groups are randomly selected. The samples from the randomly selected groups are then analyzed. A. cluster random sampling C. stratified random sampling B. systematic random sampling D. simple random sampling 5. This is a characteristic that describes the sample. A. parameter B. population C. sample D. statistic 6. It pertains to the characteristic that describes the population. A. sample B. population C. statistic D. parameter 7. This is a term in Statistics which pertains to the subgroup of a population. A. parameter B. population C. sample D. statistic 8. Which of the following is an example of a parameter? A. H C. $2 D. X9. Which of the following is an example of a statistic? A. Jupiter has 67 confirmed moons. B. There are 24 senators in the Philippine Senate. C. Only 5 randomly chosen learners won the cash prize. D. The Philippines consists of 7, 107 islands. For #10-13, refer to this given population (2, 7, 9) _10. What is the population mean in the given data above? A. 18 B. 6 C. 4.9 D. 2.45 11. What is the population variance of the data set? A. 8.67 B. 2.94 C. 2.45 D. 18 12. Find the population standard deviation of the data set. A. 8.67 B. 2.94 C. 2.45 D. 18 13. Compute the mean u, of a sampling distribution of means of the data set. A. 2.45 - . B. 4.9 C. 6 D. 18 14. If the population variance of a data set is 7. 01, what is its population standard deviation? A. 2 B. 2.64 C. 2.65 D. 7.01 15. Find the My of a sampling distribution of means of a sample consisting of values 3,3,6. A. 16 B. 14 C. 12 D. 4 Additional ActivityWhat's New Activity: Pair Me! This activity will help you recall and explore the different terms/symbols that you will encounter in learning the concepts on problem solving on random sampling. Match the symbols from column A to its word in column B which were tackled in the previous module. Write your answer in the space provided before the number. Column A Column B 1 . S a. Population mean 2. 02 b. Sample standard deviation 3.5 c. Population standard deviation 4. u d. Sample mean 5 . My e. Population variance Join me in exploring the main concepts of this module. 5Assessment Choose the best answer. Write the letter of your choice in CAPITAL LETTERS on the space provided. (15 points) 1. How many possible of size n = 3 can be drawn from a population of size 12? C. 144 D. 220 A. 36 B. 1,728 2. Which symbol is used for population mean? D. 02 8 A. Al B. . HX C 62 3. What is the finite population correction factor if the size of the population is 200 and the sample size is 25? A. 0.979 B. 0.879 C. 0.938 D. 0.856 4 Which symbol is used for standard deviation of the population? A. H B. HX C 62 D. o 5. Which of the following statements is correct? A. The mean of the sampling distribution of the means is less than the population mean. B. The mean of the sampling distribution of the sample means is greater than the population mean. C. The means of the samples drawn from a population are always equal to the population mean. D. The means of the samples drawn from a population may be equal, greater than or less than the population mean. For numbers 6 - 10, a population consists of the data (1, 2, 3, 4). 6. How many different samples of size n = 2 can be drawn from the population? A. 6 B. 5 C. 4 D. 3 _ 7. Which of the following sample means is the most frequent in the sampling distribution of sample means? A. 1.5 B. 2 C. 2.5 D. 3 8. What is the probability of the sample mean 3.5 in the sampling distribution of sample means? A. 2 A I w D. 2 9. What is the lowest value of the sample mean in this sampling distribution? A. 0 B. 1.5 C. 2 D. 2.5 1610. Which of the following histogram correctly shows the sampling distribution of sample means of size n = 2? A. C. 2 T alt 0 1.5 2 2.5 3 3.5 0 1.5 2 2.5 3 3.5 B. D. WIN ALMAIN AIGAL WIT 0 2 2.5 3 3.5 4 0 2 2.5 3 3.5 4 For items 11-15, refer to the data below: A population consist of five (5) measurements 2, 3, 5, 6 and 7. 11. What is the mean? A. 3.44 B. 4.60 C. 5.20 D. 4.92 12. What is the variance of the population? A. 3.44 B. 4.60 C. 5.20 D. 4.92 13. How many different samples of size n = 2 can be drawn from the population? A. 7 B. 8 C. 9 D. 10 14. What is the mean of the sampling distribution of the means (MY)? A. 3.44 B. 5.20 C. 4.60 D. 4.92 15. What is the variance of the sampling distribution? A. 3.90 B. 0.89 C. 2.20 D. 1.298 Assessment Answer the following multiple-choice questions to see if your understanding of the concepts in this module have improved. For Nos. 1 to 6: The mean weight of sachet of 3-in-1 coffee is 20 grams with a standard deviation of 1.2 grams. A sample of 36 sachets is taken from the production line. 1. What is the mean of the sampling distribution of sample means? a. 17 C . b . 20 d. 36 2. What is the variance of the sampling distribution of the sample mean? a. 0.04 C . b. 0.20 d. 25 3. What is the standard deviation of the sampling distribution of the sample mean ? a. 0.04 b. 0.20 d. 25 4. What is the probability that the mean of a random sample of 36 sachets of coffee will have a mean weight that is less than 19.6 grams? a. 0.0228 C. 0.5400 b. 0.4772 d. 0.9772 5. What is the probability that the mean of a random sample of 36 sachets of coffee will have a mean weight that is greater than 19.6 grams? a. 0.0228 C. 0.5400 b. 0.4772 d. 0.9772 6. What is the probability that the mean of a random sample of 36 sachets of coffee will have a mean weight that between 19.5 and 20.3 grams? a. 0.0606 C. 0.4938 b. 0.4332 d. 0.9270 7. If a population has a mean of 4.87, what is the mean of the sampling distribution of its sample means? a. 2.21 C. 4.87 b. 2.44 d. 9.748. If a population has a standard deviation of 9.7, what is the standard deviation of the sampling distribution of its means? The sampling distribution was derived with sample size n = 16. a. 0.61 C. 2.43 b. 1.65 d. 5.14 9. Which of the following is the reason why the sampling distribution of the sample mean is a normal distribution? a. The variance of the population is small. b. The sample size is large C. The sample is taken from a normal population. d. The Central Limit Theorem guarantees that the sampling distribution of the sample mean is normal regardless of the distribution of the population where the sample was taken. 10. Consider a population consisting of values 2, 3, 5, 7. What is the population standard deviation? a. 1.92 C. 3.69 b. 2.22 d. 4.92 11. Which of the following statements is NOT true about the Central Limit Theorem? a. When a population does not have a normal distribution, the distribution of the sample means will approximately be normal if a large number of samples is taken. b. When the population has a normal distribution, the distribution of the sample means will be uniform for any sample size c. The larger the sample size from a population is, the better the approximation of a normal distribution. d. The Central Limit Theorem allows us to answer questions about sample means using the normal distribution, even if the population is not normal. 12. Suppose that a population consists of the values 1, 2, 3, 4, 5, and 6. Samples of size 2 are taken with replacement from this population. How many samples of size two are possible? a. 6 C. 30 b. 12 d. 36 For Nos. 13 to 15: Suppose that a sample size of 100 is taken from a population with mean 500 and standard deviation of 80. 13. What is the probability that the sample mean lies in the interval (490, 510)? a. 10.56% C. 78.88% b. 39.44% d. 89.44%