Assignment_2 (1)

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Stockton University *

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5150

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Statistics

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Jan 9, 2024

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Assignment 2 1. Find ¯ x and s for these two small data sets. Check your answers with technology (JMP). Note: The goal of this exercise is to get you comfortable with computing ¯ x and s by hand, if you find that you feel comfortable computing ¯ x and s after Data A, feel free to just generate only JMP output for the second one, as the calculations by hand can be quite time consuming. Data A 9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74 Data B 6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 5.56, 7.91, 6.89, 12.50 For 2. and 3. find the answers by hand first and then generate summary stats in JMP. Show your work. 2. In the annual ”Great Pie-Eating Contest,” 31 contestants are given a random number of pies to consume in the shortest time possible. After the contest, the organizers want to know how the contestants fared and plan for next year’s event. They’ve asked you to analyze the data and provide some insights. Here’s the dataset representing the number of pies each contestant ate: 10, 5, 7, 8, 12, 14, 6, 3, 9, 20, 15, 1, 16, 4, 13, 11, 19, 2, 18, 17, 22, 25, 23, 21, 24, 27, 28, 26, 30, 29, 31 The organizers have a few questions for you: i) What’s the median number of pies eaten by the contestants? ii) Can you provide the five-number summary to help them understand the distribution of pie consumption? iii) What’s the difference between the number of pies eaten by the contestant who ate the most and the contestant who ate the least? ( Hint: Range ) iv) To encourage more contestants next year, they want to award a special prize to the con- testant who ate the most pies while maintaining a healthy digestion rate. What’s the highest number of pies a contestant ate without exceeding the third quartile (Q3)? ( Hint: Idea of ”the middle 50%”, in order to avoid extreme values that can occuse at the beg- gining/end of data) 3. In a secret laboratory hidden deep within an abandoned amusement park, eccentric scientist Dr. Quirkovitch conducted a bizarre experiment involving quantum bananas. He wanted to understand if bananas, when subjected to quantum physics principles, could predict the future. As part of his experiment, he recorded the number of quantum bananas consumed by 20 lab rats during one of his peculiar sessions. 1

Here’s the dataset representing the number of quantum bananas consumed by each lab rat: 42, 37, 88, 5, 3, 99, 101, 2, 77, 33, 18, 1, 8, 111, 7, 66, 55, 123, 6, 9 Dr. Quirkovitch has some questions for you: i) What’s the median number of quantum bananas consumed by the lab rats during the exper- iment? ii) Can you provide the five-number summary to help Dr. Quirkovitch understand the distri- bution of quantum banana consumption among his lab rats? iii) Dr. Quirkovitch is concerned about the potential quantum fluctuations in banana consump- tion. Check for suspected outliers. iv) In a truly unhinged twist, Dr. Quirkovitch wants to award the ”Quantum Oracle” title to the lab rat who consumed the most bananas without collapsing the banana wave function. How many quantum bananas did this rat consume, and do they qualify for the title? What do you get when you mix Star Wars and banana bread? Bananakin Skywalker. 4. The National Health and Nutrition Examination Survey (NHANES) is a unique survey that combines interviews and physical examinations. It includes basic demographic information; questions about topics such as diet, physical activity, and prescription medications; as well as the results of a physical examination measuring a variety of variables, including blood pres- sure and cholesterol levels. The program began in the early 1960s, and the survey currently examines a nationally representative sample of about 5000 persons each year. You will work with the total cholesterol measurements (mg/dL) obtained from participants in the survey in 2009–2010. To examine changes in cholesterol with age, we consider only the 3044 participants between 20 and 50 years of age and have classified them into the three age categories 20s, 30s, and 40s. Please find Cholesterol.jmp on Canvas. i) Whip out your best graphs and number crunching skills (summary stats). Now, when it comes to cholesterol’s little dance with age, let’s see if it’s behaving like a fine wine or more like a rollercoaster ride. Buckle up, folks, because we’re about to uncover the age-old secrets of cholesterol’s journey through time. You can generate several graphs and see which one gives you a better representation of your data. Hint: I’d go with one that starts with B- and ends with -oxplot. ii) Let’s give these distributions a bit of a critique, shall we (Comment on shapes)? Feel free to spill the beans on any funky curves or misfit values that caught your eye. Remember, in the world of data, it’s not a party until someone brings the weirdness! (Comment on outliers) iii) The ideal range of total cholesterol is below 200 mg/dL. For individuals with elevated cholesterol levels, prescription drugs are often recommended to lower levels. Among the 3044 participants between 20 and 50 years of age, 4 individuals in their 20s, 24 individuals in their 30s, and 117 individuals in their 40s were taking prescription medications to reduce their choles- terol levels. How do you think your comparison of the distribution would be changed if none of the individuals were taking medication? Explain. 2

5. The Fortune Global 500, also known as the Global 500, is an annual ranking of the top 500 corporations worldwide as measured by revenue. In total, the Global 500 generated $ 31.2 tril- lion in revenues in 2014. Fortune Global.jmp on Canvas provides a list of the 30 companies with the highest revenues (in billions of dollars) in 2014. i) Fire up the data carnival ride in JMP and let’s get wild! Create a histogram and then go ahead and analyze its personality—tell me if it’s got curves that make rollercoasters jealous and a center that’s as focused as a squirrel on an acorn hunt! (Generate a histogram in JMP, and determine its shape and center). ii) Which measures of center and variability would be appropriate for this distribution? Why? iii) Hit that summary statistics button in JMP like you’re summoning a data wizard! Now, tell me, what’s the real superstar, the true typical value (the data diva)? And did your estimation come close or miss the mark like a blindfolded dart throw? Let’s find out if you’re a data fortune teller or a data disaster. (Generate summary statistics in JMP, what is the true typical value (measure of center)? How close were you with your approximation?) 6. Businesses know that customers often respond to background music. Do they also respond to odors? Nicolas Gu´ eguen and his colleagues studied this question in a small pizza restaurant in France on Saturday evenings in May. On one evening, a relaxing lavender odor was spread through the restaurant; on another evening, a stimulating lemon odor; a third evening served as a control, with no odor. Scents.jmp on Canvas shows the amounts (in euros) that customers spent on each of these evenings. i) Generate the boxplots and compare the three distributions. ii) Brace yourselves for a plot twist that’s wilder than a squirrel on an espresso binge! What’s giving you that eyebrow-raising ’I did not see that coming’ vibe in not one but two of these boxplots? Why? Hint: Look at the five number summary closely iii) Were both odors associated with increased customer spending? 3

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Assignment_2 (1)

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