STAT
Exam1 A_F18_Key-1.pdf

# Iii 3pts variable of interest whether a student will

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iii. [3pts.] Variable of interest: Whether a student will attend Dr. Sargent’s guest lecture and seminar or not. iv. [3pts.] Population parameter: The proportion of all fall 2018 ISU students that would attend Dr. Sargent’s guest lecture and seminar. v. [3pts.] Sample statistic: 578/693 (457/605 Form B); or the proportion of fall 2018 stat 226 students that would attend Dr. Sargent’s guest lecture and seminar. (b) [3pts.] Is the sample obtained in this survey representative of the population of interest? Ex- plain why or why not. No, The sample consists of only undergraduate students. We would need a sample that consists of both undergraduate students and graduate students. Stat 226 consists primarily of business students who have some knowledge/interest in the economic field; therefore, they may be more interested in attending his seminar than other students at ISU, ie. there is a bias. Also, there is no mention of a random process being used to select the students for the survey, which is another indication the sample is not representative. 2. [3pts.] Variable types. Give an example of an ordinal categorical variable . Briefly explain your answer. Answers will vary. Examples include school grade classification; education level; likert scale or any kind of preferences. No credit given for nominal categorial variables. -score:

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Exam I Stat 226 Fall 2018 —KEY Page 4 3. Highway Mpg. A United States car manufacturer is attempting to develop a model that has the highest miles per gallon (mpg) on the highway. The company gathered data of 93 cars on the road and a statistical consultant calculated their average highway mpg. The histogram and the summary statistics of the data collected are shown below. Use the JMP output provided to answer the following questions. (a) [4pts.] For each of the percentiles below, define the corresponding quartile and report its value. Quartile Value Quartile Value 25 th Percentile: Q 1 26 ; 50 th Percentile: Q 2 28 (b) [2pts.] For the distribution estimated by the histogram provided in the JMP output, i. would you choose the MEAN or the MEDIAN to describe its center (location)? ii. would you choose the VARIANCE or the IQR to describe its variability? (c) [2pts.] Clearly explain your choices in question 3b. The histogram indicates a possible right skew distribution. Since the mean and variance are sensitive to outliers, the median and IQR would be better to report in this case. (d) [5pts.] Report the IQR and explain the IQR in the context of the data. IQR = 31 - 26 = 5 Explanation in context: The range of the middle 50% of the highway mpg data is 5 mpg. (e) [2pts.] Comment on the modality and presence of outliers for the histogram provided in the JMP output: i. Modality: Unimodal ii. Presence of outliers (circle one from the choices below): Potentially on the right Potentially on the left None Cannot determine -score:
Exam I Stat 226 Fall 2018 —KEY Page 5 4. Chess Ratings. Arpad Elo was a physics professor at Marquette University who developed a chess player rating system based on the Normal distribution. Player rating systems based on his work are common in two-player (or two-team) games. Every player is assigned a numerical rating level

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