d9e5e56a227e7c07633a6115210405bb377a8fc6

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Simon Fraser University *

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103

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Statistics

Date

Feb 20, 2024

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Uploaded by MinisterGrasshopperMaster522

1 STAT 203-OL01 Practice Midterm Examination 2024- Feb- 13, 7:00- 8:30 PM at B9201 • On the cover page, neatly print your name as it appears in Canvas and your student ID number within the indicated boxes. Include only one letter or one number per box. If your name is too long, you can complete writing it to the right of the boxes. • This is a closed book test, but you are allowed one sided handwritten aid sheet of US letter sized paper with as much on it as you want. • This midterm covers chapter 1-6, 8, 9. • You are allowed to use a non-graphic calculator . • Your work for Part II will be marked for clarity of explanation. • Do NOT write on or near the QR code on any page. • Y ou must write this exam independently, and hand in your own work , failing to do so could result in failure of a course or even suspension from SFU. DDAF2476-C2F7-45E5-BB80-56D5FCBDF72A pt1 #1 Page 1 of 10 First name (please write as legibly as possible within the boxes) Last name Student ID number

2 Part I [10 pts]: Multiple-choice questions , please ensure that you mark the correct choice of each question in the bubble sheet provided. The marking process is based only on the bubble sheet only. I-Q01. [1 pt]. The 137 horses in a study on enteroliths, a type of stone in the gut, were housed either in a small paddock, a large paddock, a stall, or a grass pasture. Based on the bar chart, the percent of horses living in paddocks, large or small, is approximately: A. 38% B. 51% C. 58% D. 74% I-Q02. [1 pt]. A group of four friends has a median age of 22. Three of the friends are ages 20, 18, and 24. The age of the fourth friend must be: A. 22. B. 24 or older. C. 18 or younger. D. None of these choices are correct; we can’t tell from the information provided. I-Q03. [1 pt]. Since 2000, the median wage in the United States has risen by 1%, while the median wage for every educational subgroup: high school dropouts, high school graduates, college graduates, and people with advanced degrees has decreased. This apparent contradiction is an example of: A. extrapolation. B. Simpson's paradox. C. causation. D. correlation. 4E3A681A-1855-47E9-8DA1-3AFF3ECBAFC8 pt1 #1 Page 2 of 10

3 I-Q04. [1 pt]. A statistics professor bought a new car for $35,000. For the next 5 years, she used several automotive web pages to estimate the value of the car. She then found the least-squares regression line for the data to be ! " = 35035.71 − 4142.86 # . The correlation coefficient was − 0.99 and the scatter plot also indicates a linear association. Would it be accurate to use this equation to predict the value of the car after 10 years? A. Yes, because the correlation is very strong. B. Yes, because the x and y are strongly correlated in a linear relationship. C. No, because the value of cars is unpredictable over time. D. No, because that would be extrapolation. I-Q05. [1 pt]. Many economic variables have distributions that are single-peaked and skewed to the right. The mean and median sales prices of new homes sold in the United States in July 2019 were $209,259 and $248,756. Which of these numbers is the mean, and which is the median? Explain how you know. A. The mean is $248,756, and the median is $209,259. House prices are right skewed, so the mean will be larger than the median. B. The mean is $248,756$and the median is $209,259. House prices are left-skewed, so the mean will be larger than the median. C. The mean is $209,259and the median is $248,756. House prices are right skewed, so the median will be larger than the mean. D. The mean is $209,259and the median is $248,756. House prices are left-skewed, so the median will be larger than the mean. I-Q06. [1 pt]. If X and Y are categorical variables, one way to identify whether there is a relationship between them is to: A. calculate the correlation between $ and % . B. draw a scatterplot of the $ and Y values. C. make a two-way table of the X and Y values. D. All the above options are correct. I-Q07. [1 pt ]. Suppose that # is a Normally distributed random variable with an unknown mean & and known standard deviation 6. Approximately, 95% of the observations will lie within a distance of ___ from & . A. 6 B. 12 C. 0.6 D. 1.2 02F6A337-2B0C-4391-A0DC-57855E8B663D pt1 #1 Page 3 of 10

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4 I-Q08. [1 pt]. Suppose you received a score of 91 out of 100 on exam 1. The mean was 79 and the standard deviation was 8. What score do you need on exam 2 to do equally well, if the mean is 60 and the standard deviation is 12? A. 78 B. 91 C. 95 D. 84 I-Q09. [1 pt]. In an experiment to determine if a new type of fertilizer is better than the current "standard" fertilizer for growing corn, 20 plots of land were randomly assigned one of the two types. At the end of the growing season, the corn yields for each plot were measured. It was found that plots located closer to the highway had smaller yields than other plots. The following year, the experiment was redone, but the plots were randomly assigned to either the new or old fertilizer according to the distance from the highway. The new experiment was A. Completely randomized design B. Blocked randomized design. C. A matched pair experiment. I-Q10. [1 pt ]. Without any calculation, which of the following sets of five numbers has the smallest standard deviation. A. 7,8,9,10,11 B. 5,5,5,5,6 C. 0,0,10,10,15 D. 1,2,4,5,6 Part II. Short Answer questions. II-Q01 [5 pts] For each of the statements below, circle TRUE if the stamen is true, otherwise circle FALSE. N (1) [1 pt] For a categorical variable, a pie chart or a bar graph can be used to display its distribution. [TRUE] [FALSE] (2) [1 pt] For a histogram, there must no gap between bars. [TRUE] [FALSE] (3) [1 pt] The correlation, r, can’t describe a nonlinear relationship between two numerical variables. [TRUE] [FALSE] (4) [1 pt] For a dataset with X and Y, we fit a simple linear regression model treating Y as the response variable and X as the explanatory variable. The data point ( #̅, ! )) always lies on in the least-square regression line. [TRUE] [FALSE] (5) [1 pt] A scatterplot can only involve two numerical variables. [TRUE] [FALSE] 150E4320-E325-4D79-97C6-A7F613019748 pt1 #1 Page 4 of 10

5 II-Q02 [5 pts]. The exam scores for 300 students in an introductory statistics course are Normally distributed with a mean of 78 points and a standard deviation of 8 points. Use the 68-95-99.7 rule for parts (a) and (b) and refer to the Standard Normal Table B provided at the end for part (c). (a) [2 pts] Calculate the proportion of students who scored less than 70 points. Provided detailed calculations or include a sketch to illustrate your answer. (b) [1 pt] Determine the proportion of students who scored more than 78 but less than 94 points? Include detailed calculations in your answer. (c) [2 pts] Find the proportion of students who scored more than 84 points. Show detailed calculations to support your answer. 76579E4A-6F63-4FF7-B0B2-0C241F555EA1 pt1 #1 Page 5 of 10

6 II-Q03 [10 pts]. We are interested in answering the research question: Is a person’s MRI count predictive of his or her intelligence? To address this question, some researchers (Willerman, et all, 1991) collected a data on a sample of n = 38 college students. • PIQ : performance IQ scores (PIQ) from the revised Wechsler Adult Intelligence Scale. This variable served as the investigator’s measure of the individual’s intelligence. • MRI : Brain size based on the count obtained from MRI scans (given as count/10,000) A scatter plot indicates that PIQ and MRI are linearly associated. The sample correlation between PIQ and MRI is r = 0.3778. The sample mean and sample standard deviation for both variables are organized a table. Answer the following questions and round your answer up to 4 decimal digits. (a) [1 pt] For the question, which variable is the response variable, PIQ or MRI? (b) [2 pts] Is PIQ and MRI positively or negatively correlated? Why? (c) [2 pts] If we run a simple regression to address the question asked, denote the fitted equation as ! " = , + .# , find the slope and intercept, b and a, respectively? Show details of calculation. (d) [2 pts] What is the residual at this observation (MRI=92, PIQ=124.60)? 0AC21555-E4A4-4247-B496-3AE360CD494E pt1 #1 Page 6 of 10

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7 (e) [3 pts] What is / ! ? How effective is the regression model for these data? II-Q04 [5 pts ]. The given table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class: freshman, sophomore, junior, or senior, and by their opinion of campus residence quality: high quality, medium quality, or low quality. Answer the following questions with details of calculation. (a) [2 pts] Determine the percent of all students who responded that are sophomores? (b) [2 pts] Of the students who feel campus residences are of high quality, what percent are seniors? (c) [1 pt] Part (a) and (b), which one is an example of a conditional distribution? 83233A58-0731-438B-A83B-76974DF432AB pt1 #1 Page 7 of 10

8 89F03013-BC38-4545-87DE-2545EF10FE4E pt1 #1 Page 8 of 10

F78E6772-5FAD-4202-B039-B94C357D3EBE pt1 #1 Page 9 of 10

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