ECN221- Homework1

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Arizona State University *

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221

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Economics

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Feb 20, 2024

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ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 HOMEWORK 1 150 points ECN 221 – SUMMER 2023 B Due July 7 th 11:59PM Trying to solve homework is a great way to understand the material better, so try your best and contact me with any questions ! NOTE: PLEASE WRITE THE ANSWERS ON A SEPARATE WORD DOCUMENT OR PDF FILE THAT YOU SEND TO ME VIA EMAIL ON JULY 7 TH 11:59PM AT THE LATEST. MAKE SURE THAT THE SUBJECT OF YOUR EMAIL IS: ECN221- ‘your name’– HW1” SHOW YOUR WORK WHENEVER I ASK YOU TO OR YOU WILL GET ONLY PARTIAL CREDIT! 1. In a questionnaire, respondents are asked to mark their gender as Male or Female. The scale of measurement for gender is ________ scale. (2 pts) a. Ordinal b. Nominal c. Ratio d. Interval 2. Give an example of a variable that has a ratio scale and another one that has an interval measurement scale. What differentiates a ratio scale from an interval scale? Explain how the variables you chose meet these criteria. (5 pts) An example of an interval would be test scores. Test scores are usually #/100 which would satisfy the requirement for it to be considered an interval. An example for ratio scale would be age. Age satisfies the true zero because if someone’s age is zero then they are not born or are still in the womb. 3. The set of measurements collected for a particular element are called: (2 pts) a. Variables b. Observations 1

ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 c. Samples d. Populations 4. Data collected at the same, or approximately the same point in time are _____ data: (2 pts) a. Time series b. Approximate time series c. Cross sectional d. None of the above 5. In a sample of 50 students that are graduating ASU, 20% of them are business majors and 80% of them are art majors. The 20% is an example of: (2 pts) a. A sample b. A population c. Statistical inference d. Descriptive statistics 6. A cumulative frequency distribution is: (2 pts) a. A tabular summary of a set of data showing the relative frequency b. A tabular summary of a set of data showing sums of frequencies c. A tabular summary of a set of data showing the frequency of of items in each several overlapping classes d. A graphical device for presenting categorical data 7. The relative frequency of a class is computed by (2 pts) a. Dividing the midpoint of the class by the sample size b. Dividing the frequency of the class by the midpoint c. Dividing the sample size by the frequency of the class d. Dividing the frequency of the class by the sample size 8. The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 2

ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 10 - 19 80 20 - 29 200 30 - 39 100 a. What is the relative frequency for students working between 0-9 hours per week? Show your work. (5 pts) 20/400=.05*100= 5% b. Create a new column that shows cumulative frequency. Show your work. (7 pts) Less than 9: 20 Less than 19: 100 Less than 29: 300 Less than 39: 400 c. What is the percentage of students with at least 20 hours? Show your work. (5 pts) 200+100=300/400= .75 * 100= 75% 9. The measure of location which is the most likely to be influenced by extreme values in the data set is the: (2 pts) a. Range b. Median c. Mode d. Mean 10.Welcome to the enchanting world of mystical creatures known as "Magical Gems." Your quest is to unveil the hidden statistical secrets of their unique powers. Get ready for an exhilarating journey! Here are the magical power levels (in arbitrary units) of a group of 20 Magical Gems: 12, 8, 10, 9, 15, 12, 7, 10, 10, 15, 16, 12, 8, 11, 14, 9, 10, 8, 9, 13 7,8,8,8,9,9,9,10,10,10,10,11,12,12,12,13,14,15,15,16 Your task is to embark on a magical statistical adventure and calculate the following measures to unlock the mysteries of their powers: a. Mean: Calculate the average power level of the Magical Gems. (5 pts) Mean: 218/20= 10.9 3

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ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 b. Mode: Discover the most common power level among the gems. (5 pts) Mode: 10 c. Range: Determine the difference between the lowest and highest power levels. (5 pts) 16-7=9 d. Variance: Unleash the magical variability among their powers. (5 pts) ((7-10)^2+3(8-10)^2+3(9-10)^2+4(10-10)^2+(11-10)^2+3(12-10)^2+(13- 10)^2+(14-10)^2+2(15-10)^2+(16-10)^2)/(20-1) = 7.79 e. Median: Find the gem that represents the middle power level. (5 pts) 10 f. Coefficient of Variation: Reveal the relative variability in their powers. (5 pts) 7.79^1/2=2.79/10= .279*100= 27.9% Embrace the magic and compute these measures to uncover the statistical secrets of the Magical Gems! Show your calculations and let the enchantment guide you through each step . 11.Admission Rates to Prestigious University Programs Consider a prestigious university that offers two highly sought-after programs, Economics and Mathematics. The university receives applications from two High Schools: Constance Billard School and Sunnydale High. Constance Billard School: Economics: 400 applications, 80 admitted Mathematics: 200 applications, 60 admitted Sunnydale High: Economics: 300 applications, 200 admitted Mathematics: 500 applications, 350 admitted a. Calculate the admission rates for Economics and Math separately within Constance Billard School and Sunnydale High. Compare the results. Does Simpson's Paradox occur in this scenario? Explain. (7 points) CBS economics acceptance rate= (80/400)*100= 20% CBS Mathematics acceptance rate= (60/200)*100= 30% SH Economics acceptance rate= (200/300)*100 = 66.67% 4

ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 SH Mathematics acceptance rate= (350/500)*100 = 70% b. Calculate the overall admission rates for Economics and Mathematics when the results from Constance Billard School and Sunnydale High are combined. Compare these rates with the admission rates calculated separately for each group. Discuss any inconsistencies or surprises you observe. (7 points) Economics = (280/700)*100 = 40% Mathematics = (410/600)*100 = 68.33% c. How does the difference in the number of applications between Constance Billard School and Sunnydale High contribute to the occurrence of Simpson's Paradox in this scenario? Explain the relationship between subgroup sizes and the overall admission rates for Economics and Mathematics. (7 points) There is a higher acceptance rate for the mathematics program and CBS has 1/3 of the number of applicants compared to Sunnydale High. This makes it seem like not a lot of people are getting accepted by CBS because the majority is applying to Economics, which has a lower acceptance rate d. Reflect on the implications of Simpson's Paradox in the context of university admissions. What challenges or biases might arise when making decisions based on aggregated data without considering subgroup analysis? How can universities address this issue? (5 points) If we look at the data without comparing the overall admissions for each major, then it makes it seem like the university is favoring kids from Sunnydale High, which can lead to a lawsuit. Universities can show both sides of the analysis to show that there is no bias and it is just because of the number of applicants to each major. 12.A set of exam scores has a mean of 70 and a standard deviation of 5. Find the Z-score for a student who scored 85 on the exam. Show your work. (5 points) (85-70)/5 = 3 13.The distribution of test scores is approximately normal with a mean of 75 and a standard deviation of 12. What percentage of students scored above 90 on the test? Show your work. (5 points) (90-75)/12=1.25 Put into excel =NORM.DIST(1.25,0,1,1) to get 0.89 | 1-0.89= 0.11 or 11% 5

ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 14.If a data point has a Z-score of 1.8, how many standard deviations is it from the mean? (2 points) It is 1.8 standard deviations above the mean 15.In a normally distributed dataset, approximately what percentage of data points have Z-scores between -1 and 1? (2 points) Approximately 68% of data points lie between a z-score of -1 to 1 in a normally distributed dataset 16.The weights of a sample of people are normally distributed with a mean of 160 lbs and a standard deviation of 20 lbs. If an individual has a Z-score of -1.5, what is their weight? Show your work. (5 points) Z-score= (x- 𝜇)/ 𝜎 so -1.5= (x-160)/20 | -30=x-160 | x= 130 The individuals weight would be 130 pounds 17.I give you a list of Netflix movies that are on the Netflix streaming platform in the file “NetflixOriginals” that you can find on Canvas. In this dataset, you have the name of the movie, genre, premiere date, runtime, IMDB score, and language of the movie. Download the dataset and complete the following tasks: a. In a new sheet, create a pivot table that shows the frequency, relative frequency, and percent frequency of each genre of these movies. (5 pts) x b. Create another pivot table in a new sheet that has only the percent frequency of each genre of these movies. (4 pts) x c. Using that table, create a bar chart and a pie chart of the percent frequency. (5 pts) x d. In a new sheet, create another pivot table that shows the cumulative frequency, cumulative relative frequency, and percent cumulative frequency of IMDB scores for these movies. (5 pts) x e. Group the IMDB scores into 10 classes where the lowest score is 2.5 and highest is 9. (5 pts) x Now, I want you to answer the following questions: f. What is the mean, median, Q1, and Q3 values of the sample IMDB scores and runtime in the dataset? Show your work. (5 pts) Runtime: Mean- 93.58 Median-97 Q1-86 Q3- 107.75 6

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ECN221 Stephanie El Khoury Summer B - 2023 Homework 1 IMDB scores: Mean- Median- Q1-5.7 Q3- 7 Runtime Q1- (25/100)(584+1)= 146.25 | Q3- (75/100)(584+1)= 438.75 IMDB scores Q1- (25/100)(584+1)= 146.25 | Q3- (75/100)(584+1)= 438.75 g. What is the standard deviation and variance of the sample IMDB scores and runtime in the dataset? Show your work. (5 pts) Runtime SD- 27.76 Variance- 770.71 IMDB SD- 0.98 Variance- 0.96 Standard Deviation- Square root of variance Variance- (The number – The mean)^2……. h. What is the covariance and correlation between the sample IMDB scores and runtime ? Show your work. (5 pts) Runtime Covariance-769.39 Correlation- 1 IMDB scores Covariance-0.96 Correlation- 1 Correlation Formula: 𝜌𝑥𝑦 = ( 𝜎𝑥𝑦) /( 𝜎𝑥𝜎𝑦) Covariance Formula: 𝜎𝑥𝑦 = [∑(𝑥𝑖−𝜇𝑥)(𝑦𝑖−𝜇𝑦)]/(𝑁) Work shown in excel For questions a, b, c, d, and e please send me the excel file you have created as an attachment with your homework email. For questions f, g, and h you can compute the values using excel, but I want you to write in the word/pdf file the equations you use. 7

ECN221- Homework1

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