Grade/Strand: FINDING THE MEAN AND VARIANCE OF THE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN AND DEFINING SAMPLING DISTRIBUTION OF THE SAMPLE MEAN FOR NORMAL POPULATION Directions: Encircle the letter of the best answer on your answer 1) Which of the following is described as the quotient of the population variance and the sample size n? 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 2) Which of the following is the notation used for the variance of the sampling distribution of the sample mean? A. U B. O- C. o' D. H 3) Which of the following is the formula used to determine the variance of the sampling distribution of the sample mean? A. G = 9. 1-n n N-1 C. 0? = E P(X ) - (X-H) ] B. O2 S? N +1 D. 0= = = P( N) -(X-W) ] For numbers 4-8, please refer to the problem below. A population of a certain LGBTQ+ community is consist of six (6) measurements 2, 3, 6, 9, 11, and 5. 4) What is the mean of the population? A. 10 B. 8 C. 6 D. 5 5) What is the variance of the population? A. 10 B. 8 C. 6 D. 5 6) How many different samples of size n = 4 can be drawn from the population? A. 20 B. 15 C.8 D. 7) What is the mean i of the sampling distribution of the sample mean? A. 4 B. 5 C. 6 D. 7 8) What is the variance of the sampling distribution of the sample mean? A. 4 B. 3 C. 2 D. 1 9) This distribution is used to determine the probability of an event by transforming the mean of the sample to an approximately standard normal variable when the population variance is given. A. t-Distribution C. Chi-Square Distribution B. Z-Distribution D. Pearson Correlation Coefficient 10) Which of the following notations is used for the mean of the population? A. U B. H C. O D. C 11) A population consists 11, 19, 22, 2, 8, 9, and 15. Suppose samples of 2 are drawn from this population. This situation is an example of the sampling distribution of the sample mean for a normal population with population variance is A. unknown B. known C. large D. small 12) This is used to determine the probability of an event by transforming the mean of the sample to a variable of this distribution where the population variance is unknown, and the sample size is less than 30. A. t-Distribution C. Chi-Square Distribution B. Z-Distribution D. Pearson Correlation Coefficient 13) Which of the following formulas is used to calculate the population standard deviation? A. 0? = (H-X)2 N C. s? = - B. O? D. 02 = 2(X-H)2 N 14) Given p = 88, X = 90, s = 2, and n = 15. This is an example of sampling distribution of the sample mean for a normal population when the population variance is A. unknown B. known C. large D. small 15) A researcher used to develop a problem-solving test to randomly selected 100 Grade 11 students. From this sample, the mean and standard deviation is 90 and 4 respectively. The mean of the population is 88. The researcher is in a situation of the sampling distribution of the sample mean wherein the population variance is A. unknown B. known C. large D. small Prepared by:Name: Date Gra defStra nd: CENTRAL LIMIT THEOREM Directions. Choose the letter that corresponds to the correct answer. Encr'rcle the letter ofyour answer. 1 . 10. 11. 12. 13. Which of the following is correct about the sampling distribution of the sample mean using the Central Limit Theorem? A The mean of the sampling distribution of the means is not equal to the mean of the population. B. As the sample size it increases the sampling distribution of the means approaches a normal distribution. C The variance of the sampling distribution of the means is equal to the variance of the population multiplied by the sample size n. D. The standard deviation of the sampling distribution of the means is equal to the standard deviation of the population multiplied by the square root of the sample size :1 Which of the following statements best describes a z-value? A. The z-value leads to the area under the curve found in the normal curve table. B. The z-value leads to the area under the curve found in the normal distribution table, which is a probability. C. The z-value leads to the area under the curve found in the normal curve table, which is a percentage, and that percentage gives the desired probability for X. D. The Z-value leads to the are under the curve found in the normal curve table, which is a probability, and that percentage gives the desired percentage for X. Who is the French-born Maiematician who proved the first version of the Central Limit Theorem? A. Abraham de Moivre C. Aleksander Lyapunov B. Aristotle D. Rene Descartes According to the Central Limit Theorem. which sample size will give a smaller standard error of the mean? A. Ir' B. 12 C. 23 D.40 If a population is not normally distributed, the distribution of the sample means for a given sample n will . A. be positively skewed C. takethe same shape as the population B. be negatively skewed D. approach a normal distribution as n Increases The mean and standard deviation of a population are 1'5 and 15, respective1y. The sample size is 100. What is the standard error of the mean? A. 1.5 3.1.73 C. 0.15 D.El The mean and standard deviation of a population are 400 and A0, respectively. Sample size is 25. What is the mean of the sampling distribution? A. 400 B. 40 C. 25 D. B The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams. Which of the following will you use? A. Normal Distribution C. Discrete Probability Distribution B. Central Limit Theorem D. Binomial Distribution In a study done on a life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5 3 years. If a sample of 50 people from this region is selected. and the probability that the mean life expectancy will be less than 70 years, which of the following will you use? A. Normal Distribution C. Discrete Probability Distribution B. Central Limit Theorem D. Binomial Distribution Which of the following refers to the standard deviation of a sampling distribution? A. It is the sum of squares B. It is the standard error of the mean C. It only applies only to population data. D. It can be larger than the standard deviation for the population. What is the standard deviation of sampling distribution if standard deviation of population is 35 and sample size is 9? A 11.6? 3.12.6? C 1367 0.1467 If a population has a mean of 6.5, what is the mean of the sampling distribution 01 its means? A 56 B.65 CjIr 0.65 The mean and standard deviation of a population are 200 and 20, respectively. What is the probability of selecting 25 data values with a mean less than 190? A. 69% B. 31% C. 0.62% D. 99% For numbers 14-1 5, refer to the problem below. Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. Assume that the average sleep hour is normally distributed, and 35 high school students are randomly selected. 14. 15. Compute the z-score for 6 hours of sleep. A. 1.04 B. 0.18 C. 0.52 D. 0.32 What is the probability that a randomly selected group of 35 high school students gets more than 6 hours of sleep each night? A. 0.3503 B. 0.1492 C. 0.0714 D. 0.4236