After going te, you are expected 1. illustrate the factors which affect the sample size determination; 27. C 2. compute for the required sample size using the formula; and 3. solve problems involving sample size determination. 38. A 39. A What I Know 40 Let us see how far you will go and how much you know about this pretest. Please answer all questions with all your best and utmost honesty so that we can gauge your learning in the target competency of this lesson. Let's get started! NOTE: For students with online connections and want to have a paperless assessment, please go to the link given by your teacher. Direction: Choose the letter of the correct answer for each item. Shade/ blacken the circle that corresponds to your chosen answer. A B 1. Which of the following factors is not considered in the O O determination of sample size? A. margin of error B. level of confidence C. confidence interval D. variance or standard Deviation B C D 2. The value of confidence coefficient ( ) of 1.645 is used O O O O in sample size determination if a researcher wants to be confident that the parameter is within the estimate. A 99 B. 95 C, 92 D. 90 3273. How does the level of confidence affect the sample size? (Consider that other factors are constant) A . The higher the level of confidence, the smaller the sample size required. B. The lower the level of confidence, the larger the sample size required. C. The lower the level of confidence, the smaller the sample size required. D. The sample size remains constant in every level of confidence. OD B D 4 . O Which of the following is the correct equation for sample size determination? ( Za/2 ) +(0 ) ] ect: A. n= x - Zazz ( Jm) C. n = VTIC B. n = X+ E D. n= [ (zazz ) (o)] on 5. How does the margin of error and sample size affect one another? (Assume that the other factors are constant) A. A smaller sample size reduces the margin of error. B. A higher margin of error requires a larger sample. C. A lower margin of error requires a larger sample size. D. A small sample size results in a lower margin of error. on D 6. How does standard deviation o affect the sample size? O (Assume that the other factors are constant) A. The sample size is constant for all values of o. B. Lower o reduces the required sample size. C. Lower o increases the required sample size. D. Higher o decreases the required sample size. 7. A researcher wants his estimate with a minimum margin of error. Which of the following is suggested? A. Reduce the sample size. B. Use a sample size of 30. C. Increase the sample size. D. Use a sample size of less than 25. A C D 8. How large is the sample size required so that a researcher to O is 98% confident with the estimate of a sample, of standard deviation 5, that the error will not be more than 2? A. 6 B. 34 C. D. 84 A BCD 9. If a 95% level of confidence is applied by the researcher in O O O O the condition given in item # 8, what sample size shall be obtained? A. 8 B. 17 C. 24 D 34 328For questions 10 to 15, refer to the situation that follows The diameter of the coconuts harvested in a local farm in Quezon Province is normally distributed with a population standard deviation of 8 mm. At a 95% level of confidence, a researcher wants to have an estimate that will not be more than 3 mm from the TRUE population average diameter of the coconuts. A B O 0 O .D 10. What correct confidence coefficient should be applied to determine the required sample size? A. 2.576 B. 2.33 C. 1.96 D. 1.645 A B 11. What is the given population standard deviation from the O O situation? B. 16 C. D. 64 B C D 12. What is the desired margin of error for the estimate of the O population parameter? A. 2 B. 3 C. 4 D. 16 A B C 13. What minimum sample size shall be used by a researcher O O to meet the expected results? (Round up to the nearest whole number) A. 16 B. 28 C. 62 D. 107 A B C D 14. If the researcher wishes to reduce the error of the O O O estimate, what should be done? I Consider a larger sample. II Reduce the level of confidence III Increase the level of confidence. A. I only C. I and II only B. II only D. I and III only A B C D 15. What sample size is needed for the situation to have a O O O O margin of error not more than 1? (Round to the nearest whole number) A. 87 B. 102 C. 246 D. 425 How do you find the pre-test? Did you encounter both familiar and unfamiliar terms, symbols, and notations? Kindly compare your answer in the Answer Key on the last part of this module. If you obtain 100% or a perfect score, skip the module and immediately moveStandard Deviation (o) =6 Then using the formula, you will have, n = [ (zay, )( " = [execon* = [1358] = [4.6613 = 2172 Therefore, the nurse needs at least 22 infants to be enrolled in the study to be 98% confident that the true mean weight of newborn infants is within 3 ounces of the sample mean. What's More Apply the knowledge you obtained from the discussion by solving the given problems below. 1. A 99% confidence interval has to be created to estimate the mean volume of contents in the bottles of Honey-Z. Assume that the population standard deviation is 20 ml. Calculate the sample size needed if the margin of error is no more than: a. 6 ml b. 5 ml G. 4 ml d. 3 ml 3332. How large sample size is required to determine the mean IQ of seventh graders of Luis Palma National High School within +3 points, population standard deviation of 15, and with the following confidence level? a . 98% b. 95%. Nar C. 90%. d. 80%. What I Have Learned To summarize what you have learned from this module try completing the following statements. Write the correct word or phrase in a separate sheet of paper. 1 . is a process of finding the number of elements to be drawn from a population to create sub-group called sample, subject for a study. 2. The sample size is determined by the equation. 3. In the formula/ equation for the sample size, n is the required sample size, Zo, is the represents the 15 . and is the margin of error. 4 . The factors which influence the sample size determination are and 5. As the sample size gets larger, the margin of error gets 6. The level of confidence determines how certain you want to be that the parameter fall within your confidence interval. The more confident you want to be, the the sample size needs to be. What I Can Do Read the following problems carefully. Apply your skills in solving the following cases. 1. A researcher found that the IQ scores of the ALS students in the Division of Quezon Province are normally distributed with a mean of 110 and a standard deviation of 10. a. How many ALS students are needed to test so that the estimate will not be more than 5 from the population mean with a 99% level of confidence? b. Due to limited contact with ALS students, the researcher tested a small number of ALS students. Explain the effect of this small sample on the estimate of the parameter? 2. A confidence interval estimate has a maximum error of 2.50. If the distribution of the data where the estimate is obtained is normal with a standard deviation of 9, . How many samples are considered in 98% confidence interval estimate for the mean? b. What must be done to the sample size to reduce the margin of error of the confident interval estimate? Support your answer. Assessment Direction: Choose the letter of the correct answer for each item. Shade/ blacken the circle that corresponds to your chosen answer. A B D 1. The following are the factors to consider in the O O O determination on sample size EXCEPT for the A. Margin of error C. confidence interval B. Level of confidence D. variance or standard deviation 334OD O O 2. The value of confidence coefficient ( Za, ) of 1.96 is used in sample size determination if a researcher wants to be % confidence level that the parameter is within the estimate. Name: A 99 B. 95 C. 92 D Section: 90 C O D 3. How does the level of confidence affect the sample size? (Consider that other factors are constant) A. The higher the level of confidence, the smaller the sample size required. B. The lower the level of confidence, the larger the sample size required. A C. The lower the level of confidence, the smaller the sample size required. D. The sample size remains constant in every level of confidence. D 4. Which of the following is the correct equation for sample C O size determination? [(2012 ) (0 ) ] . B A. n= x- Za/2 (7,) C. n = a . D B. n = X + E D. n = df + 1 10 . 5. How does the margin of error and sample size affect one 11 . o to C D another? (Assume that the other factors are constant) A. A smaller sample size reduces the margin of error. B. A higher margin of error requires a larger sample. C. A lower margin of error requires a larger sample size. D. A small sample size results in a lower margin of error. C D 6. How does the standard deviation (o) affect the sample size? (Assume that the other factors are constant A. The sample size is constant for all values of o. B. Lower o reduces the required sample size. C. Lower increases the required sample size. D. Higher o decreases the required sample size. B C D 7. A researcher wants his/her estimate with a minimum O O O margin of error. Which of the following is suggested? A. reduce the sample size. B. use a sample size of 30. C. increase the sample size. D. use a sample size of less than 25. B C D O 8. How large is the sample size required so that a researcher is 99% confident with the estimate of a sample, of standard deviation 5, that the error will not be more than 2? A. 6 B. 13 C. 42 D. 84 335A B 9 . If a 90% level of confidence is applied by the researcher C D in the condition given in item # 8, what sample size shall be obtained? B. 17 C. 27 D. A. 8 34 For questions 10 to 15, refer to the situation that follows. The diameter of the coconuts harvested in a local farm is normally distributed with a population variance of 64 mm. At a 99% level of confidence, a researcher wants to have an estimate that will not be more than 2 mm from the TRUE population average diameter of the coconuts. ABCD 10. What correct confidence coefficient should be applied to O O determine the required sample size? A. 2.58 B. 2.33 C. 1.96 D. 1.645 B C 1 1. What is the given population standard deviation from the O O O D situation? A. 8 B. 16 C. 24 D. 64 A B 12. What is the desired margin of error for the estimate of the O population parameter? A. 2 B. 3 C. 4 D. 16 B C D 13. What sample size shall be used by a researcher to meet the O O O expected results? (Round up to the nearest whole number) A. 16 B. 32 C. 62 D. 107 A B C D 14. If the researcher wishes to reduce the error of the estimate, O O what should be done? I Consider a larger sample. II Reduce the level of confidence III Increase the level of confidence. A. I only C. I and II only B. II only D. I and III only A. B C D 15. What sample size is needed for the situation to have a O O margin of error not more than 1? (Round to the nearest whole number) A. 87 B. 102 C. 347 D. 427