SOCI 311 Spring 2020 Syed Hammad Ali Final Exam Total Marks: 75 Name: Part A: Short Answer Questions - [40 Marks] 1. Which of the following statements best described the relationship between the independent and dependent variables? Explain your answer in no more than 3 lines. [2 Marks] A) The independent variable in the population is the equivalent of the dependent variable in the sample. B) The value of the dependent variable depends on the independent variable. C) The dependent variable is to univariate statistics what the independent variable is to bivariate statistics. D) The independent variable in the sample is the equivalent of the dependent variable in the population. E) The dependent variable always precedes the independent variable in time. 2. Which of the following are continuous levels of measurement? Explain your answer in no more than 3 lines. [2 Marks] A) Nominal and ordinal B) Nominal, ordinal, interval, and ratio C) Ordinal, interval, and ratio D) Ordinal and interval E) Interval and ratio 3. What level of measurement would you use to describe the following immigration categories of individuals: Skilled Worker, Canadian Experience Class, Entrepreneur, Provincial Nominee, and Family Sponsored? Explain your answer in no more than 3 lines. [2 Marks] 4. If there are 30 teams in the NHL and 6 are Canadian, what is the probability of a Canadian team winning the Stanley Cup in any given year? Show calculation [2 Marks] A) 0.8 B) 0.5 C) 0 D) 0.2 E) 1 5. Benjamin asked 780 fellow undergraduates to identify the capital of British Columbia. Of those sampled, 468 knew the capital but had never travelled there, 273 both knew the capital and had travelled there, and 39 did not know the capital but had travelled there. Based on this data, if Benjamin were to randomly select another undergraduate to test, what is the probability that he/she would both know the capital city is Victoria and have travelled there? Show calculations [2 Marks] A) 0.95 B) 0.35 C) 0.05 D) 0.75 E) 0.6 6. If a variable is normally distributed, what percentage of all observations lies between 1 standard deviation from the mean? Explain your answer in no more than 3 lines. [2 Marks] A) 68.26 per cent B) 81.5 per cent C) 49.5 per cent D) 75 per cent E) 95 per cent 7. What is the area between the mean and a z-score of 3.33? No explanation required. [2 Marks] 8. Yves has collected data in a survey that measures individuals' knowledge of hydraulic fracturing, a natural gas extraction technique. He found that within a sample of 15,000 people, the mean score of respondents was 5.25 (roughly 5 questions out of 25 were answered correctly) with a standard deviation of 2.1. If the distribution was standardized, what would be the value of the mean? Explain your answer in no more than 3 lines. [2 Marks] A) 0.21 B) 0.00 C) 2.1 D) 3.15 E) 5.25 9. Oscar decided he wanted to measure the happiness of Canadian individuals who are married. To make sure his respondents did not hold anything back, each spouse was questioned separately. He interviewed 7 couples first and then another 32. If you were to conduct a t-test, what would the degrees of freedom be? Show calculations [2 Marks] A) 78 B) 39 C) 38 D) 224 E) 77 10. Maxine works full-time at a Montreal comic book shop. She wants to determine how many customers have mentioned the latest commodity over the course of three months. In her sample, she finds a standard deviation of 222. Compared to a standard deviation of 2, a standard deviation of 222 is more likely to have which of the following? Explain your answer in no more than 3 lines. [2 Marks] A) Large standard error B) Small sample size C) Little variance D) Small standard error E) None of the above 11. At what sample size do the differences between z-values and t-values become extremely minimal? Explain your answer in no more than 3 lines. [2 Marks] A) 300 B) 120 C) 50 D) 90 E) 150 12. Which of the following is an example of a null hypothesis? Explain your answer in no more than 3 lines. [2 Marks] A) There is no significant relationship between x and B) There is no significant difference between x and C) x is greater than D) Both A and B E) All of the above 13. Vanessa knows that the average grade in her statistics class is 70 per cent. She samples her study group and finds that its members have an average grade of 75 (standard error = 3.4). Calculate t. Show calculations [2 Marks] 14. On a measure of collectivist values, East Asian immigrants that had been in Canada between 5 to 10 years had a mean score of 12, and West Asian immigrants that had been in Canada between 5 to 10 years had a mean score of 9. The anticipated level of error between the measurements of the two sample means was 1.7. What is the z-score of the difference between the two means? Show calculations [2 Marks] A) 0.2 B) 1.8 C) 1.3 D) 2.6 E) 3.4 15. Which of the following methods can be used for all levels of measurement? Explain your answer in no more than 3 lines. [2 Marks] A) Pearson's r B) Chi-square test of statistical significance C) ANOVA D) Gamma 16. Which of the following relies exclusively on rank? Explain your answer in no more than 3 lines. [2 Marks] A) Cramer's V B) Pearson's r C) Lambda D) Spearman's rho E) Gamma 17. What is the denominator in the gamma formula? No explanation required. [2 Marks] A) Nsame - Ndifferent B) Nsame * Ndifferent C) (Nsame * Ndifferent)2 D) [Nsame (Nsame Ndifferent)]2 E) Nsame + Ndifferent 18. What does a Pearson's r value of zero indicate? Explain your answer in no more than 3 lines. [2 Marks] A) A perfect negative relationship between variables B) A perfect positive relationship between variables C) That there is no sampling error D) That there is a perfect correlation between variables E) None of the above 19. Allie attended a privately funded post-secondary educational institution in Western Canada. She surveyed her professors to measure if there was a relationship between the number of years they had spent in the public education system and the number of hours they now dedicate to their students in their new positions within the private system. She found that r = 0.71. What does this suggest? Explain your answer in no more than 3 lines. [2 Marks] A) A positive relationship where all of the observed values lie on the line of best fit B) A positive relationship where few of the observed values lie on the line of best fit. C) A negative relationship where all of the observed values lie on the line of best fit. D) A negative relationship where few of the observed values lie on the line of best fit. E) None of the above 20. Which of the following distributions does ANOVA use? No explanation required. [2 Marks] A) A-distribution B) Z-distribution C) T-distribution D) L-distribution E) F-distribution Part B: Calculations - [35 Marks] 1. A researcher believed that increase income leads to increase happiness. Both variables' scales are from 1 - 10 (higher value indicates more income and happiness). She gathered the following data: X = Income Y = Happiness Response number 1 2 3 4 5 6 Total X 2 3 4.5 5 7 10 Y 1 5 7 6 8 9.5 X2 4 9 20.25 25 49 100 Y2 1 25 49 36 64 90.25 XY 2 15 31.5 30 56 95 a) Complete the above table and then calculate Pearson's r. Show all calculations [6 Marks] b) What is the strength and direction of the correlation? Explain your answer in no more than 5 lines [4 Marks] 2. Brianne, who is struggling in her statistics class, is advised by her professor to spend more time studying before exams. Brianne is curious to know if this conventional wisdom (i.e., that more hours spent studying improves academic performance) is true. In order to find out, Brianne randomly selects 5 classmates and records the number of hours they spent studying for their last exam alongside their exam grades. Following are the tables she makes: Student 1 2 3 4 5 Student 1 2 3 4 5 Number of hours spent studying 4 0 6 1.5 3 Number of hours spent studying Exam grade 4 72 0 46 6 80 1.5 67 3 70 Rank 2 5 1 4 3 Exam grade 70 46 80 67 73 Rank 3 5 1 4 2 a) Calculate D2. Show calculations [2 Marks] b) Calculate Spearman's rho. Show calculations [3 Marks] 3. Women once had a significantly higher life expectancy than men in Canada, but some researchers believe this is changing. A researcher hoping that this is the case decided to first see if there were similar numbers of males and females in young and older age brackets before running more in-depth analysis. Using data from the 2011 Census, he found the following information: Manitoba Population 2011 Census by Age and Sex Sex Child Senior Total Males 118,620 (a) 75,285 (b) 193,905 Female 112,540 (c) 97,170 (d) 209,710 Total 231,160 172,455 403,615 a) Complete the following table and calculate the value of chi-square. Show all calculations [6 Marks]: Group a b c d Total fo 118,620 75,285 112,540 97,170 fe (fofe)2 ( ) b) Is there a significant difference between the observed frequencies and the expected frequencies with an that equals 0.05? Why or why not? Explain your answer in no more than 5 lines [4 Marks]: 4. In the Aboriginal Peoples Survey, 2012: Social Determinants of Health for the OffReserve First Nations Population, 49 per cent of Mtis people surveyed over the age of 15 (n = 8,801) reported their health as excellent or very good, while 61 per cent within the total Canadian population reported the same. a) We want to know if the proportion of the Mtis population over age 15 who report their health as excellent or very good is lower than that of the total Canadian population by a statistically significant amount. What would the hypotheses be for this data? [2 Marks] H0: H1: b) What would be the zobtained? Show all calculations [5 Marks] c) Is zobtained significant at a confidence level of 95 per cent? Why or why not? Explain your answer in no more than 5 lines [3 Marks]