Quiz 3 Review

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3000

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Jan 9, 2024

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Quiz 3 Review ● Office hours cancelled today. ○ Tomorrow 10:00 - 11:00 am, 2:00 - 3:00 pm ● On Friday, we’ll finish Unit 12 during class time. ● No class next Monday. ● Quiz 3 is due on Friday at 11:59 pm. ○ I recommend working on the quiz on Friday between 9:30-5:00 when there is an instructor on duty. Which type of test should you use on Quiz 3? Chi-squared goodness of fit test ● One categorical variable ● There’s a claim about the distribution of a categorical variable. Is the proposed model a good fit? ● Example: We know the distribution of housing options for the UGA population (66% off-campus, 28.5% on-campus, and 5.5% Greek). Is the distribution the same for BUSN students? ○ Housing is the only variable, because our sample only included BUSN students. Chi-squared test of independence ● Two categorical variables ● Is there a relationship between two categorical variables? ● Example: Is there a relationship between the size of the choice set and whether someone stops at a tasting booth?

T-test for the regression slope ● Two quantitative variables ● Is there a relationship between two quantitative variables? ● Example: Is there a relationship between the age of a car (in years) and its price? F-test for the overall regression model ● Multiple quantitative variables ● Is there at least one useful predictor in the model? ● Example: Can we use opening weekend revenue, production budget, and number of theaters to predict total revenue? Formulas for test statistics, degrees of freedom and expected values are given on the reference sheet. Scenario A. A prospective home buyer sampled 13 homes that were for sale just north of Lake Macatawa in Michigan and recorded the prices (in dollars) listed on the real estate website Zillow. They also recorded the size of each home in square feet. 1. Suppose we want to analyze the relationship between the size of the homes and the prices. Which type of test is appropriate? 2. The sample slope is $212/sq ft, but you want to calculate a 95% confidence interval for the population slope. Calculate the critical value using the JMP distribution calculator. Scenario B Quality Source Defective Acceptable Total Vendor 1 14 112 126 Vendor 2 20 60 80 Vendor 3 22 150 172 Total 66 262 328 3. Which type of test would you use to analyze the relationship between vendor and quality? 4. Calculate the expected number of defective shipments from Vendor 1. Scenario C. The human resources department of a large corporation suspects that people are more likely to call in sick on Monday or Friday so they can take a long weekend. They take a random sample of 850 sick-day reports from the past few years and determine the day of the week for each report. The table below shows the counts for each day of the week. Day Monday Tuesday Wednesday Thursday Friday

# of sick-day reports 192 151 148 152 207 5. Which type of test would you use to test whether people are equally likely to call in sick on all five days of the week? 6. The test statistic for this dataset is 17.7765. Calculate the p-value. Test 3 JMP reference sheet ● To analyze the distribution of one variable: Analyze - Distribution ○ Chi-squared goodness-of-fit test ● To analyze the relationship between two variables: Analyze - Fit Y by X ○ Chi-squared test of independence ○ Correlation / regression ● To make predictions using multiple explanatory variables: Analyze - Fit Model ○ Multiple regression Mixed JMP Practice The dataset amazon-books.jmp contains information about 325 books for sale at amazon.com. Download the data here: https://tinyurl.com/3000-amazonbooks The dataset includes two prices for each book: List Price (the price set by the publisher) and the Amazon Price . The variable Large Discount indicates whether the discount offered by amazon.com is 25% or higher. 1. Is there a relationship between the list price and the Amazon price? Choose an appropriate statistical method to answer this question. a. Chi-squared goodness-of-fit test b. Chi-squared test of independence c. t-test for the regression slope 2. Describe the association between the list price and Amazon price in this sample: As list price increases by $1, the Amazon price is predicted to increase by ____ . 3. Calculate the correlation that could be used to describe the strength and direction of the relationship between List Price and Amazon Price. 4. What can be said about the quality of this model’s predictions? ____ % of the variation in Amazon book prices is explained by this model. 5. A representative from Amazon claims that they offer a large discount half the time. Does this

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data support that claim? Choose an appropriate statistical method. a. Chi-squared goodness-of-fit test b. Chi-squared test of independence c. t-test for the regression slope 6. In this sample, what proportion of books had a large discount on Amazon? 7. Calculate the test statistic that you would use to test the claim that Amazon offers a large discount half the time. Note: Chi-squared tests are always two-sided 8. Is there a relationship between how the book is bound (hardcover/paperback) and whether Amazon offers a large discount? Choose an appropriate statistical method to answer this question. a. Chi-squared goodness-of-fit test b. Chi-squared test of independence c. t-test for the regression slope 9. For the test chosen above, show that the conditions for inference are met. The conditions for inference are met, because the smallest expected count is _____ , which is larger than 5. 10. Calculate a p-value to test for an association between how the book is bound (hardcover/paperback) and whether Amazon offers a large discount. Use all six quantitative variables in the dataset (number of pages, year of publication, height, width, thickness, and weight) to predict the price of the book on Amazon. Careful: Make sure you are using the Amazon Price not the List Price. 11. What test statistic would you use to decide whether the overall model is useful? Do not round. 12. Based on backward regression, what variable(s) should you remove from the regression model? Only select the variable(s) you would remove in the first step of backward regression.

Quiz 3 Review

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