Read and analyze the following situations. Determine whether the following statements have a known (or can be computed) or unknown population variance. Also, identify the formula to be used for the standard error of the mean by writing o,, when the population variance is known and s, when the population variance is unknown.

A BCD 1. Which of the following measures the dispersion of the O O O O sampling distribution of the sample mean and is calculated using the relation E(X - M)2 . P(X) or E[X2 P(x)] - u2? (1 point). A. mean of the sampling distribution of sample mean B. variance of the sampling distribution of the sample mean C. standard deviation of the sampling distribution of the sample mean D. average deviation of the sampling distribution of the sample mean ABCD 2. Which of the following is the notation used for the mean 0 0 0 0 of the sampling distribution of sample means? (1 point) A. M C. o B. Mx D. Ox A BCD 3. Which of the following equations is the formula used to OO0 0 determine? A. Ox = 1 -n Vn VN-1 C. of = ZIP(X) . (X - 1)2] B. oz 1-n D. of = ZIP(X) . (M - X)2] N N-1O D O O O O For numbers 4-8, please refer to the problem below. and 7. A population consists of five (5) measurements 2, 3, 6, 5, A. 3.44 4. What is the mean of the population? (2 points) B. 4.60 C. 4.92 D. 5.20 A C O O 5. What is the variance of the population? (2 points) A. 3.44 C. 4.92 B. 4.60 D. 5.20 A B C D O O O 6. How many different samples of size n = 2 can be drawn from the population? (2 points) A. 7 C. 9 B. 8 D. 10 A B C OU O O O 7. What is the mean of the sampling distribution of the sample means? (3 points) A. 3.44 C. 4.92 B. 4.60 D. 5.20 O O O 8. What is the variance of the sampling distribution of the sample means with a sample size of 2? (3 points) A. 0.89 C. 2.20 B. 1.29 D. 3.90situation: Joe, a DOH COVID-19 tracker, found out that the number of infected persons of COVID-19 in seven low-risk provinces of the country are 1, 9, 2, 12, 8, 7, and 10. Suppose that 5 provinces are drawn as sample. 1. What is the mean (u), variance (62) and standard deviation of the population (o)? 2. How many different samples of size n =5 can be drawn from the population? List them with their corresponding mean. 3. Construct the sampling distribution of the sample mean. 4. What is the mean (My) of the sampling distribution of the sample mean? Compare this to the mean of the population. 5. What is the variance of the (o,) of the sampling distribution of the sample mean?A B C D 1. This distribution is used to estimate population parameters O O O when the population variance is unknown, and the sample size is less than 30. A. Z-Distribution B. t-Distribution C. Chi-Square Distribution D. Pearson Correlation Coefficient A B C D 2. Which of the following notations is used for the standard 0 0 0 0 deviation of the sampling distribution of the sample mean? A. ul C. o B. MX D. Ox B C D 3. Which of the following equations is the formula used to O O O transform the sample mean to an approximately standard normal variable Z when the population variance is known? A. Z = x - H C. z = x - M S B. z = X - H D. z = A BCD 4. The mean weight of two thousand (2000) 11-year-old children O O O O is 35 kilograms with a standard deviation of 5 kilograms. Samples of 25 children were selected and the mean weight of this group was found to be 34 kilograms with a standard deviation of 3 kilograms. What condition of the samplingdistribution of the sample mean for normal population manifests in the situation? A. Population variance is known B. Population variance is unknown C. Sample standard deviation is small B C O 5 D. Sample standard deviation is large O O Which of the following formulas is used to calculate the standard deviation of the sampling distribution of the sample mean when the population standard deviation is unknown? A. ON =. Vn N +n VN-1 C. S. = B. Of = B D. Of = -s+1 C D Vn O O O 6. O A population consists 1, 9, 2, 12, 8, 7, and 10. Suppose samples of size 5 are drawn from this population. This situation is an example of the sampling distribution of the sample mean for a normal population wherein population variance is A. unknown C. large B. known D. small A B C D 7 . O O O O Suppose that the rice mill wants to test its product to find out whether it meets the average weight of 50 kilograms Twenty-five sacks of rice are weighed and found to have an average weight of 49.8 kg with a standard deviation of 0.12 kg. The rice mill owner is in a situation of the sampling distribution of the sample mean wherein the population variance is A. unknown C. large B. known D. small A B C 8. Suppose the manager of a Jollibee Corp. wishes to know O O O whether their chicken packaging machine still packs accurately after 6 months of use. The machine was rated to pack 1,500-gram pack of chicken with a standard deviation of 30 grams. The statistician tests a sample of 40 packs to test the accuracy of the machine. What example of sampling distribution of the sample mean for normal population portrays the situation? A. variance is known B. variance is unknown C. standard deviation is small D. standard deviation is large 9. This distribution is used to determine the probability of an A B D event by transforming the mean of the sample to an O o O approximately standard normal variable if the population variance is known and sample size is greater than 30. A. t-Distribution B. Z-Distribution C. Chi-Square Distribution D. Pearson Correlation CoefficientA B D O O O 10. Given a = 15, s = 5, and n = 16. This is an example of the sampling distribution of the sample mean for a normal population when the population variance is A. unknown B. known C. large D. small B C 11. Which of the following formulas is used to calculate the O O standard deviation of the sampling distribution of the sample mean when the population standard deviation is given? A. Oj = . IN -n Vn N-1 C. SX = Vn B. Ox =- Vn D. OF = S+1 Vn A B C D 12. Mr. Pineda administered a Mathematics Achievement Test to a O O random 45 graduating SHS students. In this example, the mean and standard deviation are 95 and 11. The population parameters are j1=89 and o=8 . What example of the sampling distribution of the sample mean for the normal population portrays the situation? A. variance is known B. variance is unknown C. standard deviation is small D. standard deviation is large A B C D 13. Given =90, X=92 s=5, and n=28. This is an example of the O O O sampling distribution of the sample mean for a normal population when the population variance is A. unknown C. large B. known D. small A B C D 14. A sample of five measurements, randomly selected from O approximately normally distributed population, resulted in the summary statistics: X=34.7, s=10.2. The population mean is equal to 36. The given data is an example of the sampling distribution of the sample mean for a normal population wherein the variance is A. unknown C. large B. known D. small A B C D 15. Given u=15, 0=5, X=12.8 and n=100. This is an example of the O O o o sampling distribution of the sample mean for a normal population when the population variance is A. unknown C. large B. known D. smallSituation Answer Standard Error Formula 1. A population has a mean of 85 and a standard deviation of 6. A random sample of 22 measurements is drawn from this population. 2. The weights of female SHS students are normally distributed with a mean of 45kg. Twenty samples consisting of 10 students are drawn from the population and found to have a mean of 46 kg and a standard deviation of 1.24kg. 2313. A random of n = 70 measurements are obtained from a population with a mean of 156 and a standard deviation of 23. 4. A manufacturer of nylon synthetic fibers for fishing line, claims that the mean tensile strength of their product is 30 1b. of a 20 meter-line. To test the claim of the manufacturer, a sample of 25, the 20- meter line was tested and found to have a mean weight of 32 1bs and a standard deviation of .78 1b. 5. Given population mean of 200, a sample of 25 has a standard deviation of 3