Homework 1-Anna Harvey

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University of Massachusetts, Dartmouth *

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500

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Statistics

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Jul 2, 2024

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Homework 1 POM 500 Statistical Analysis Note : Attempt all questions as per rubric. Problems including case study has a weightage of 10 marks each. The maximum you can score is 50. Use Excel function wherever possible. Problem-1 Using ‘VehicleFailureData’ available on the course website, answer the following: a) Classify each variable as nominal, ordinal, interval or ratio. a. Vehicle number — Ordinal because they are arranged in (ascending) order to identify an attribute of the vehicle. b. Failure Month — Interval because this is determined from 0 to a particular month in numerical form. c. Mileage at Failure — Interval because this is determined from 0 to a particular number of miles in numerical form. d. Labor Hours — Interval because this is determined from 0 to a particular number of hours in numerical form. e. Labor Cost — Interval because this is determined from 0 to a particular dollar amount in numerical form. f. Material Cost — Interval because this is determined from 0 to a particular dollar amount in numerical form. g. State — Nominal because there are abbreviations used to identify an attribute of the vehicle (in this case being the state). b) Identify qualitative and quantitative variables. a. Qualitative —State, Vehicle Number b. Quantitative —Material Cost, Labor Cost, Mileage at Failure, Labor Hours, Failure Month c) How many vehicles failed in month-9? (Write Excel function) a. 71 vehicles failed in month 9. b. Function: =COUNTIF($B$2:$B$1625,B37) d) What was the maximum labor cost? (Write Excel function) a. $3,234.41 is the maximum labor cost. b. Function: =MAX($E$2:$E$1625) e) What was the total failure cost for the data available? (Write Excel function) a. $685,836.05 is the total failure cost. b. Function: =SUM($E$2:$E$1625,$F$2:$F$1625)

Problem-2 A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug. a) This study involved the comparison of two populations. What were the populations? a. The population of women whose mothers took the drug DES during pregnancy. b. The population of women whose mothers did not take the drug DES during pregnancy. b) Do you suppose the data were obtained in a survey or an experiment? a. I would hope that the data was obtained in a survey given its nature, including the seven year time frame, the predicted side effects, etc. However, due to the fact that we are attempting to control one variable (the consumption of the DES drug) this would be much easier to collect data in an experiment and track how they influence the rate of tissue abnormality development. c) For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities. a. Sample size = 3980 Developed abnormality = 63 63 / 3,980 = 0.0158… This means that 15.8 out of every 1,000 women whose mothers did take the DES drug during pregnancy developed tissue abnormalities. d) For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities? a. 15.8 out of 1,000 for those whose mothers did take the drug. They are twice as likely than those whose mothers did not. (2) 15.8 / 2 = 7.9 So, 7.9 out of every 1,000 women whose mothers did not take the DES drug during pregnancy developed tissue abnormalities. e) Medical studies often use a relatively large sample (in this case, 3980). Why? a. By using a large sample pool, they are able to collect enough data on the number of cases that actually show correlation between the drug and the predicted or suspected outcome. This is also why they will typically take several years, in order to see these effects develop over time.

Problem-3 ACNielsen conducts weekly surveys of television viewing throughout the United States. The ACNielsen statistical rating indicates the size of the viewing audience for each major network television program. Rankings of the television program and of the viewing audience market share for each network are published each week. a) What is AC Nielsen attempting to measure? a. AC Nielsen is attempting to measure the Television rating point of each major television network. This helps show what programs that viewers of certain demographics watch most. b) What is the population? a. The population is television network program viewers in the US. c) Why would a sample be used in this situation? a. A sample would be used because it is unrealistic to take data from every TV viewer throughout the United States. It would be extremely expensive and take too much time, so sampling allows them to collect the data and carry out the experiment in a more efficient way. d) What kinds of decisions or actions are based on the ACNielsen studies? a. These studies allow the networks to see the number of people in a demographic that watch their given programs and allows them to cater their strategies more effectively. This could influence the timing of programs, commercials shown, the days the program runs, etc. It also can show them which programs are not worth continuing as they are not developing a big enough viewership.

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Problem-4 Using ‘VehicleFailureData’, summarize the data for failures in top 10 (maximum number of vehicle failures) states by constructing the following: a) Relative and percent frequency distributions STATE FREQUENCY RELATIVE PERCENT TX 293 0.290674603 29.06746032 CA 200 0.198412698 19.84126984 FL 168 0.166666667 16.66666667 GA 75 0.074404762 7.44047619 AZ 61 0.060515873 6.051587302 LA 49 0.048611111 4.861111111 NC 48 0.047619048 4.761904762 PA 43 0.04265873 4.265873016 MI 36 0.035714286 3.571428571 CO 35 0.034722222 3.472222222 TOTAL 1008 b) Bar Chart TX CA FL GA AZ LA NC PA MI CO 0 50 100 150 200 250 300 350 293 200 168 75 61 49 48 43 36 35 FREQUENCY State Number of Vehicle Failures c) Pie Chart

TX 29% CA 20% FL 17% GA 7% AZ 6% LA 5% NC 5% PA 4% MI 4% CO 3% Frequency TX CA FL GA AZ LA NC PA MI CO d) Find top three states with maximum number of vehicle failures. a. Texas b. California c. Florida Case Study: Movie Theater Releases

The movie industry is a competitive business. More than 50 studios produce hundreds of new movies for theater release each year, and the financial success of each movie varies considerably. The opening weekend gross sales ($ millions), the total gross sales ($ millions), the number of theaters the movie was shown in, and the number of weeks the movie was in release are common variables used to measure the success of a movie released to theaters. Data collected for the top 100 theater movies released in 2016 are contained in the file Movies2016 (Box Office Mojo website). Table below shows the data for the first 10 movies in this file. Performance Data for Ten 2016 Movies Released to Theaters. Managerial Report Use the tabular and graphical methods of descriptive statistics to learn how these variables contribute to the success of a motion picture. Include the following in your report. a) Tabular and graphical summaries for each of the four variables along with a discussion of what each summary tells us about the movies that are released to theaters. a. Tabular Summary i. This table provides data on 100 movies released in 2016 and include data on: “Movie Title”, “Opening Gross Sales”, “Total Gross Sales”, “Number of Theaters”, and “Weeks in Release”. Captain America: Civil War had the highest gross sales with $179.14 million, and the lowest was for Lion with $0.12 million. Rouge One: A Star Wars Story had the highest overall gross sales at $532.18 million, and the lowest being Kevin Hart: What Now? was with

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$23.59 million. Secret Life of Pets was in the most theatres at 4,381, while Manchester by the Sea was in the fewest at 1,213. The highest number of Weeks in Release was 46 for Hidden Figures , and the lowest was 7 for Ben-Hur (2016). b. Graphical Summary i. A scatter diagram or bar graph could be used to visualize the relationship in the data for opening and total gross sales. This would allow us to make comparison off values based on performance. A line graph or scatter diagram would be able to demonstrate the deviation in the numbers of theaters for each movie. A bar graph or scatter diagram could be used to demonstrate the correlation between number of theatres and overall gross sales, allowing for a easy evaluation of the success of each movie. c. Discussion i. The tabular and graphical summaries lay out the performance of the 100 movies released in 2016. Based on the data, Captain America: Civil War and Rouge One: A Star Wars Story were the most popular movies of the year based on opening and total gross sales. The correlation between total gross sales and number of theatres can demonstrate some of the factors contributing to a movie’s success. This data can help determine the advertising needs for various films based on weeks in release and number of theatres. b) A scatter diagram to explore the relationship between Total Gross Sales and Opening Weekend Gross Sales. Discuss. i. This scatter diagram shows the relationship between total gross sales and opening gross sales of movies released in 2016. The X axis represents the movie titles based on their numbered row and the Y axis represents the gross sales in millions. The orange dots represent the opening gross sales, while the yellow represent the total gross sales. According to the scatter diagram, Captain America: Civil War had the highest gross sales with $179.14 million, and the lowest was for Lion with $0.12 million. Additionally, it shows us that Rouge One: A Star Wars Story had the highest overall gross sales at $532.18 million, and the lowest being Kevin Hart: What Now? was with $23.59 million. The diagram shows that movies with high opening gross sales, tend to have higher total gross sales, however there will always be outliers like Hidden Figures which made $0.52 million in gross sales opening, and finished out at $169.61 million in total gross sales. (Diagram Below)

0 20 40 60 80 100 120 0 100 200 300 400 500 600 Total Gross Sales vs. Opening Weekend Gross Sales Opening Gross Sales ($ millions) Total Gross Sales ($ millions) c) A scatter diagram to explore the relationship between Total Gross Sales and Number of Theaters. Discuss. i. This scatter diagram shows the relationship between total gross sales and the number of theaters for movies released in 2016. The X axis represents the movie titles based on their numbered row and the Y axis represents the number of theatres is aired in. The orange dots represent the total gross sales, while the yellow represent the number of theatres. According to the scatter diagram, Secret Life of Pets was in the most theatres at 4,381, while Manchester by the Sea was in the fewest at 1,213. The diagram shows that movies with high total gross sales, tend to have been aired in more theatres. (Diagram Below) 0 20 40 60 80 100 120 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Total Gross Sales vs. Number of Theaters Total Gross Sales ($ millions) Number of Theaters

d) A scatter diagram to explore the relationship between Total Gross Sales and Number of Weeks in Release. Discuss. i. This scatter diagram shows the relationship between total gross sales and the number of weeks in release of movies released in 2016. The X axis represents the movie titles based on their numbered row and the Y axis represents the total gross sales in millions. The orange dots represent the total gross sales, while the yellow represent the number of weeks in release. According to the scatter diagram, the highest number of Weeks in Release was 46 for Hidden Figures , and the lowest was 7 for Ben-Hur (2016). The diagram shows that movies with high total gross sales, may have been in a higher number of theatres, however that is not as indicative as some of our other variables because Hidden figures did not perform nearly as well (only earning $169.61 million total) as films that were in release for significantly less like Finding Dory which was in release for 25 weeks and earned $408.08 million total gross. (Diagram Below) 0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 40 45 50 Total Gross Sales vs. Weeks in Release Total Gross Sales ($ millions) Weeks in Release

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