UNIVERSITY OF TORONTO MISSISSAUGA. SOC222 Measuring Society In-Class Test. November 11, 2011 Duration 11:15a.m. 13 :00p.m.

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1 UNIVERSITY OF TORONTO MISSISSAUGA SOC222 Measuring Society In-Class Test November 11, 2011 Duration 11:15a.m. 13 :00p.m. Location: DV2074 Aids Allowed You may be charged with an academic offence for possessing the following items during the writing of an exam unless otherwise specified: any unauthorized aids, including but not limited to cell phones, pagers, personal digital assistants (PDAs), ipods, MP3 players, or any other device. NAME: STUDENT NUMBER: SIGNATURE: EXAMINATION AIDS: One hand written formula sheet, a ruler, a calculator, pens, and pencils. You may NOT use any other materials. There are two parts to this test. Part I is multiple choice questions (35 points). Part II is short answers and hand written calculations (65 points). The normal distribution table is attached. Be sensitive to the points of the questions for allocation of your time and energy. ANSWER THE MULTIPLE CHOICE QUESTIONS IN PART I ON THE SCANTRON FORM. ANSWER THE HAND WRITTEN CALCULATION QUESTIONS IN PART II ON THE EXAMINATION BOOKLET. DO NOT ATTACH ANY OTHER PAPERS. AT THE END OF THE TEST, YOU NEED TO HAND IN (1) THIS EXAMINATION SCRIPT, (2) EXAMINATION BOOKLET, (3) SCANTRON, (4) THE FORMULA SHEET. Page 1 of 7

2 Part I: Multiple Choice (35 points, each question is worth one point) Identify the letter of the choice that best completes the statement or answers the question. 1. The purpose of inferential statistics is to acquire knowledge of the from the by means of the distribution a. population, sample, sampling b. sample, sampling, population c. inductive, empirical, stratified d. theoretical, empirical, theoretical 2. Two categories of inferential statistics are a. parameter estimation and confidence intervals; b. parameter modeling and hypothesis testing; c. confidence intervals and hypothesis testing; d. standard deviations and standard errors. 3. A Z score of indicates a score that lies a. one standard deviation unit to the right of the mean b. one standard deviation unit to the left of the mean c. 1/2 of one standard deviation unit on each side of the mean d. any of the above are possible 4. What percentage of an observation lies between the standard deviations of -2 and +1, supposing that the observation follows a normal distribution? a per cent b. 68 per cent c. 95 per cent d per cent e. 75 per cent 5. Roughly percent of the total area under the normal curve rests between the mean and one standard deviation above. a. 50 b. 40 c. 34 d Which of the following is NOT true of the normal curve? a. It can be applied to any distribution encountered by a researcher. b. It helps for interpretation of the standard deviation. c. It can be used to describe distributions of scores. d. It can be used to make statements about probabilities. Page 2 of 7

3 7. If 95% of the population has an IQ between 70 and 130, what is the probability of meeting a person with an IQ either higher than 130 or lower than 70? a.5 b.05 c. 95 d. cannot be determined 8. The standard deviation of a sampling distribution of means is: a. equal to the population standard deviation. b. greater than the population standard deviation. c. less than the population standard deviation. d. none of the above 9. The area between a negative Z score and a positive Z score can be found by a. subtracting the Z scores from each other b. subtracting each Z score from the mean and adding the results c. adding the Z scores and finding the area in the Z score table for the summed Z scores d. adding the areas between each Z score and the mean 10. Unlike the sample and population distributions, the sampling distribution is a. empirical b. theoretical c. random d. EPSEM 11. I surveyed 48 randomly-selected residents of the apartment complex where I live to determine their voting habits. I can only use this information to generalize to all the residents if a. there is evidence of a normal population distribution b. the 48 residents all have the same voting habits c. the 48 residents are equally divided in their voting habits d. the sample distribution is not normal in shape 12. What are the three distributions involved in every application of inferential statistics? a. sample, sampling, and population b. sample, stratification, cluster c. EPSEM, random, probability d. sampling, percentage, normal 13. A defining characteristic of the normal curve is that it is a. theoretical b. positively skewed c. negatively skewed d. perfectly nonsymetrical 14. The standard error of the mean is the same thing as a. the standard deviation of a sample b. the standard deviation of a population c. the standard deviation of a sampling distribution Page 3 of 7

4 d. the variance of a sample 15. In a sampling distribution of sample means, most of the sample means will a. cluster around the true population value b. be below the population mean in value c. be above the population mean in value d. not follow any particular pattern 16. The Central Limit Theorem states that as sample size becomes large a. the sampling distribution of sample means approaches normality b. the sampling distribution of sample means becomes larger c. the population distribution becomes normal d. the sample distribution becomes normal 17. Your sample size is It is safe to assume that a. the shape of the sampling distribution of sample means is normal b. the sample is representative of the population c. the population distribution is normal d. the sample distribution is normal 18. As the standard deviation of a normal distribution increases, the percentage of the area between ± 1 standard deviation will a. increase b. stay the same c. decrease d. become non-symmetrical 19. From a random sample of 300 state university students, you found that the average number of hours of study time each week is 30 with a standard deviation of 5. A point estimate of the average study time for all state university students would be a. 5 b. 30 c. 300 d. 15 ± 1 standard deviation 20. We can estimate the probability that sample means and proportions lie within a given distance of the population value because these statistics are a. unbiased b. efficient c. random d. biased 21. Two sample statistics are unbiased estimators. They are a. means and proportions b. means and standard deviations c. medians and modes d. proportions and percentages Page 4 of 7

5 22. The probability that a sample mean is within ± 1 Z of the population mean is about a..34 b..68 c..95 d In of the cases, the mean of a sample selected by EPSEM will be more than ± 3 Z's from the population mean. a. less than 1% b. more than 5% c. more than 90% d. more than 99% 24. The efficiency of a sample estimator is essentially a matter of a. accuracy b. validity c. centrality d. dispersion 25. The sizes of four samples vary as follows: Sample A, N = 100 Sample B, N = 76 Sample C, N =1000 Sample D, N = 150 Which sample will produce the most efficient estimate? a. Sample A b. Sample B c. Sample C d. Sample D 26. The more efficient the estimate, the more the sampling distribution a. is evenly spread from the mean to ± 2 standard deviations b. becomes flatter c. clusters to the right of the mean d. is clustered around the mean 27. The probability that an interval estimate does not include the population value is called a. the margin of error b. alpha c. an error d. the odds Page 5 of 7

6 28. In estimation procedures, as the alpha level decreases, the corresponding Z scores a. move closer to the mean of the sampling distribution b. move away from the mean of the sampling distribution c. become negative d. become positive 29. We have used an alpha of 0.01 to estimate the average hours of television viewing for residents in a retirement home. What is the chance that our interval estimate does not contain the true population mean? a. 99% b. 10% c. 1% d. 1/10 of 1% 30. When using sample means as estimators, we usually estimate the population standard deviation with a. the sample standard deviation b. the sampling distribution standard deviation c. the population parameter d. the Z score 31. The tails of the theoretical normal curve a. intersect with the horizontal axis between the 4th and 5th standard deviation b. intersect with the horizontal axis beyond the 5th standard deviation c. never touch the horizontal axis d. maintain the same distance above the horizontal axis beyond the 3rd standard deviation 32. The area between two negative Z scores can be found by a. adding the Z scores and finding the area below the total Z score b. subtracting the Z scores and finding the total area above the total Z score c. finding the area between each Z score and the mean and subtracting the smaller area from the larger d. finding the area between each Z score and the mean and adding the areas 33. If a Z score is 0, then the value of the corresponding raw score would be a. 0 b. the same as the mean of the empirical distribution c. the same as the standard deviation of the empirical distribution d. probably a negative number 34. The standardized normal distribution (or Z distribution) has a. a mean of 0 and a standard deviation of 1 b. a mean of 1 and a standard deviation of 0 c. a mean equal to the average of the scores and a standard deviation equal to the mean d. a mean of 1 and a standard deviation of According to the theorems on sampling distribution of sample means, we can be sure that the sampling distribution is normal if a. the sample is large Page 6 of 7

7 b. the population is small c. the sample is stratified d. the sample is normal Part II: Hand Written Calculations (65 points) Show all necessary formulas and procedures 1. (14 points) From the records of the World Health Organization, we know that the birth weight of babies is normally distributed, with a mean of 2.75 kilograms and a variance of kilograms. a). What is the probability that the next child who is born weighs more than 4 kilograms? b). What weight do the heaviest 15% of infants weigh more than, at birth? 2. (10 points) For a sample of N number of cases with a sample mean of X bar, is it correct or wrong to use the following formula for calculation of the standard score of the sample mean? Explain. z= X µ s 3. (13 points) An insurance adjuster has collected data on claims made by Canadians over the past ten years. The average claim was $1000 with a standard deviation of 115 and the distribution was normal in shape. What is the probability that the mean claim of 25 randomly selected claims is $1100 or more? 4. (11 Points) For a random sample of 178 households in a community, average TV viewing was 6 hours/day with standard deviation of 3. Develop a 95% confidence interval to provide an estimate of the mean TV viewing time a day. 5. (11 points) A sampling survey found that 25 of the 178 random sampled households consisted of unmarried couples who were living together. What is your estimation of the population of the proportion of households consisted of unmarried couples who were living together (use 95% confidence level or α=0.05)? 6. (6 points) Mary is studying the elementary school pupils in a school district with data on all its children. Roger suggests she calculate a confidence interval of the mean age of these children. Mary responds that it is not necessary. Explain why Mary is correct. Page 7 of 7