Principles of Statistics Exam 1

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Indiana University, Purdue University, Indianapolis *

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241

Subject

Mathematics

Date

Feb 20, 2024

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rtf

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2

Uploaded by cillinois1

Math 241- Exam 1 Math 241-Principles of Statistics Exam-1 (Q1) A recent newspaper article reported on Americans' eating habits. The article reported that only about one third of American adults ate 2 or more servings of fruit per day, and only 26% ate 3 or more servings of vegetables per day. Californians ate the most fruit, while Tennesseans ate the most vegetables. Question: The state that a respondent lived in is ___________ variable. Answer: Categorical --------------------------------------------------------------------------------------------------------------------- (Q2) A recent newspaper article reported on American's eating habits. The article reported that only about one third of American adults ate 2 or more servings of fruit per day, and only 26% ate 3 or more servings of vegetables per day. Californians ate the most fruit, while Tennesseans ate the most vegetables. Question: The phrase "26% ate 3 or more servings of vegetables per day" refers to what kind of variable and why? Answer: The variable could be either quantitative or categorical depending on whether the subjects were asked how many servings of vegetables per day or whether they were asked if they ate 3 or more servings of vegetables per day, respectively. *** In this scenario, it is not clear what question was asked. Suppose the question was "How many servings of vegetables do you eat per day?" The response to this question would be a quantitative variable since each response is a numerical value with the units "servings of vegetables." Alternatively, suppose the question was "Do you eat 3 or more servings of vegetables per day?" The response to this question would be a categorical variable since each response falls into a category dash namely, "yes" or "no." In either case, it would be possible to determine the percentage of respondents who eat 3 or more servings of vegetables per day. --------------------------------------------------------------------------------------------------------- (Q3) A coffee shop next to a university surveys potential customers: students selected randomly walking onto campus. The survey asked students where they live, whether they study at the library, and their weekly food budget. Question: A student's weekly food budget is a ___________ variable. Answer: Quantitative ( This is a quantitative variable because weekly food budget is numeric (its units are $).)
Math 241- Exam 2 --------------------------------------------------------------------------------------------------------- (Q4) If we want to study the relationship between two quantitative variables such as fat and calorie content of food, what type of graphical display should be made? Answer: Scatterplot (This is the only display that helps us see a possible association). (Q5) Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. “T-shirts at a store: price each, number sold” Answer(s): Price each would be the Explanatory variable and number sold would be the Response variable. In application, price would most likely be Used to Predict number sold. (Q6) What would you expect to see in the scatterplot? Choose the correct answer below. Answer: A moderate to strong negative nonlinear association b) Scuba diving: depth, water pressure Depth would be the Explanatory variable and water pressure would be the Response variable. In application, depth would most likely be Used to Predict water pressure. (Q7) What would you expect to see in the scatterplot? Choose the correct answer below. Answer: A strong positive linear association c) Scuba diving: depth, visibility Depth would be the Response variable and visibility would be the Explanatory variable. In application, depth would most likely be predicted by using visibility. (Q8) What would you expect to see in the scatterplot? Answer: A weak to moderate negative, possibly linear association All elementary school students: age, score on a reading test Answer: Age would be the Explanatory variable and score on a reading test would be the Response variable/ In application, age would most likely be Used to Predict score on a reading test.
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