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act. 1 act. 2 Assessment (Post Test) Instruction: Read and understand each item below. Choose the letter of the correct answer and write it on your answer sheet. Show your solution if necessary 1. Which of the following describes the relationship of the population mean and the mean of the sampling distribution? 1. Which of the following statements is correct? A. The mean of the sampling distribution of the sample means is less than the A. The mean of the sampling distribution of the sa e means is less than the population mean. population mean. B. The mean of the sampling distribution of the sample means is greater than the B. The mean of the sampling distribution of the sample means is greater than the population mean. population mean. C. The mean of the sampling distribution of the samples means is equal to the C. The means of the samples drawn from the population is equal to the population population mean. The means of the samples drawn from the population is not always equal the . The means of the samples drawn from the population not equal to the population population mean. mean. 2. A certain population has a mean of 10.6 and a st 10.6 and a standard deviation of 3.4. If all the 2. A certain population has a mean of 15.4 and a standard deviation of 5.6. If a possible random samples of n-5 are taken from the population, what is the mean of random sample of 5 is taken from the population, which of the following statements ling distribution of the sample means? is correct? A. equal to 10.6 C. more than 10.6 A. The mean of the sampling distribution of the sample means is equal to 15.4. B. less than 10.6 D. not equal to 10. B. The mean of the sampling distribution of the sample means is less than 15.4 C. The standard deviation of the sampling distribution of the sample means is 5.6 3. Describe sampling distribution of the means if the random samples of size n D. The standard deviation of the sampling distribution of the sample means is 15.4 become larger? A. uniformly distributed C. Exponential 3. What is the shape of the of the sam ng distribution of the means if the random B. Normal . rectangular samples of size n become larger? A. left skewed B. right skewed C. Normal D. rectangular 4. If the variance of the population is 20, what is the variance of the sampling distribution of the means of size 5 drawn from the population? 4. If the variance of the population is 10, what is the variance of the sampling A. 2 B. 4 C. 8 D. 10 B. 4.47 distribution of the means of size 5 drawn from the population? A 2 C. 1.41 D. 10 5. What is the finite population correction factor if the size of the population is 100 5. What is the finite population correction factor if the size of the population is 200 and the sample size is 25? and the sample size is 25? A. 0.870 B. 0.879 C. 0.938 D. 0.856 A. 0.979 B. 0.879 C. 0.938 D. 0.856 6. What theorem guarantees a normal sampling distribution of the sample means? 6. What is the important assumption in the Central Limit Theorem that guarantees A. Pythagorean Theorem C. The Law of Larger Number Theorem a normal sampling distribution? B. The Central Limit Theorem A. a sample that is large enough C. a standard deviation equal to 1 D. Bayes Theorem B. a large number of random samples D. the population mean equal to 1 7. A certain population has a mean of 20 and a standard deviation of 8. Sample size 16 are taken for the purpose of sampling distribution. What is the all these sample A. 12 B. 16 C. 18 D. 20 20 8. If a population has a standard deviation of 20, what is the standard error of the mean if the sample size 16 is selected? A. 4 B. 5 C. D. 7 7. A certain population has a mean of 300 and a standard deviation of 16. Sample size 32, whose means are calculated are taken to for a sampling distribution. What is the expected value of all these means? A. 8 B. 16 C. 32 . 300 8. If a population has a standard deviation of 24, what is the standard error of the mean if the sample size 16 is selected? A 16 B. 6 C. 4 D. 24 9. If sample size of 100 is selected from a population with a mean of 50 and a standard deviation of 28, what is the standard error of the mean? 9. If sample size of 100 are selected from a population with a mean of 28 and a A. 2.8 C. 4.6 D. 3.6 standard deviation of 18, what is the standard error of the mean? A 2.8 B. 1.8 C. 4.6 D. 10 10. Multiple samples with a size of 50 are taken from a known population, where u - 35 and o - 7, as the sample size increases, what should be the value of the 10. Multiple samples with a size of 35 are taken from a known population, where H-25 and o=4 , as the sample size increases, what should be the value of the means approximated mean? approximate? A. 20 B. 25 C. 30 D. 35 A. 2 B. 12.5 C. 25 D. 35 11. A researcher wants to take random samples of size 30 of a ce opulation 11. A researcher wants to take a random sample of size 40 of a certain population with a mean of 22.5 and a variance of 10.49. What is the approximate standard a mean of 23.5 and a variance of 18.49. What is the approximate standard deviation of sample means? deviation of sample means? A. 0.59 B. 0.61 C. 0.63 D. 0.6 A. 0.68 B. 4.3 C. 3.72 D. 5.4 12. A student receives an average allowance of P100 per week with a standard 12. Members of the urban poor receive an average of P1 10 per day with a standard deviation of 10. If random samples of 5 weeks are taken, what is the approximate deviation of 20. If a random sample of 25 people is taken, what is the approximate mean of the sampling distribution? mean of the sampling distribution? A. P80 B. P100 C. P 120 D. P150 A. P55 B. P110 C. P25 D. P45 For 13-15, use the problem below. For 13-15, refer to the problem below. The average precipitation for the first 7 months of the year is 19.32 inches with the standard deviation of 2.4 inches. Assume that the average 10. Multiple samples with a size of 50 are taken from a known population, where precipitation is normally distributed. 1 = 35 and o = 7, as the sample size increases, what should be the value of the approximated mean? 13. What is the probability that the randomly selected year will have a precipitation greater than 18 inches for the first 7 months? A. 20 3. 25 C. 30 D. 35 A. 0.7088 B. 0.8523 C. 0.4562 D. 0. 1258 11. A researcher wants to take random samples of size 30 of a certain population 14. What is the average precipitation of 5 randomly selected years for the first 7 with a mean of 22.5 and a variance of 10.49. What is the approximate standard months ?. deviation of sample means? B. 0.61 C. 0.63 D. 0.65 For 13-15, refer to the problem below. 12. A student receives an average allowance of P100 per week with a standard The average precipitation for the first 7 months of the year is 19.32 inches with the standard deviation of 2.4 inches. Assume that the average deviation of 10. If random samples of 5 weeks are taken, what is the approximate precipitation is normally distributed. mean of the sampling distribution? A. P80 B. P100 C. P 120 D. P150 13. What is the probability that the randomly selected year will have a precipitation greater than 18 inches for the first 7 months? For 13-15, use the problem below. A. 0.7088 B. 0.8523 C. 0.4562 D. 0. 1258 The age distribution of senior high school students approximates 14. What is the average precipitation of 5 randomly selected years for the first 7 = normal distribution. The mean age of the grade 11 students is 17 years months? old with a standard deviation of 2.98. Sixty students are randomly A. 19.32 inches B. 22.4 inches C. 20.52 inches D. 15.56 inches selected for a sampling distribution of the sample means. Answer the following questions indicated below: 15. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months? A. 0.8907 B. 0.2587 C. 0.4156 D. 0.2879 13. What is the probability that the randomly selected has a mean age of sampling distribution that is above 16 years old? Test items are adopted and collated from Belecina, 2016, page 136-137 and from 0.9953 B. 0.4953 C. 0.0047 D. 0.5399 quipperschool.com 14. What is the probability that the mean age of the sampling distribution of the randomly selected is above 18 years old? 0.9953 B. 0.4953 C. 0.0047 D. 0.5399 15. What is the probability that the mean age of the randomly selected is within 16 to 18 years old? A. 0.9953 B. 0.9906 C. 0.0047 D. 0.5399