Statistics Milestone 1: Answers Include Rationale and the Concept

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Statistics Milestone 1 Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neigh... borhoods across the country. The plot shows a strong positive correlation. Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. • Average income per household • The number of cars on the road • Average mileage per vehicle • The number of citizens in the United States RATIONALE 2 The scatterplot below shows the relationship between the grams of fat and total calories in different food items. The equation for the least-squares regression line to this data set is . What is the predicted number of total calories for a food item that contains 25 grams of fat? • 417.56 • 483.55 • 383.55 • 549.54 3 John, the owner of an ice-cream parlor, collects data for the daily sales of ice cream with respect to the daily temperature. If John were to create a scatterplot, all of the following will be characteristics of correlation EXCEPT ___________. • Strength of association between the daily sales and temperature • Degree of association between the daily sales and temperature • Amount of daily sales at any given temperature • Direction of association between the daily sales and temperature 4 For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223. Select the correct slope and y-intercept for the least-squares line. • Slope = -0.35 y-intercept = 10.9 • Slope = 0.35 y-intercept = 10.9 • Slope = 0.35 y-intercept = -10.9 • Slope = -0.35 y-intercept = -10.9 5 Which of the following scatterplots shows a correlation affected by non-linearity? • • • • 6 Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth. • $4.00 / lb. • $7.75 / lb. • $6.25 / lb. • $0.13 / lb. 7 Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x. What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable? • The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm. • The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm. • The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm. • The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm. 8 Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below. Using the best-fit line, approximately how much money would a 45-year-old teacher make? • $50,000 • $55,000 • $48,000 • $58,000 9 A correlation coefficient between average temperature and ice cream sales is most likely to be __________. • between 0 and 1 • between 1 and 2 • between –1 and –2 • between 0 and –1 10 Which of the following is a guideline for establishing causality? • Keep all variables the same to get duplicate results. • Do not consider other possible causes. • Look for cases where correlation exists between the variables of a scatterplot. • Check if the effect is present or absent when the response variable is present or absent. 11 Which of the following statements is TRUE? • A high correlation is insufficient to establish causation on its own. • A correlation of 1 or -1 implies causation. • If the two variables of a scatterplot are strongly related, this condition implies causation between the two variables. • Only a correlation equal to 0 implies causation. 12 Raoul lives in Minneapolis and he is planning his spring break trip. He creates the scatterplot below to assess how much his trip will cost. Which answer choice correctly indicates the explanatory and response variables for the scatterplot? • Explanatory variable: Minneapolis Response variable: Miles flown • Explanatory variable: Cost Response variable: Distance • Explanatory variable: Distance Response variable: Cost • Explanatory variable: Miles flown Response variable: Minneapolis 13 Which of the following scatterplots shows an outlier in the y-direction? • • • • 14 A bank manager declares, with help of a scatterplot, that the number of health insurances sold may have some association with the number of inches it snows. How many policies were sold when it snowed 2 to 4 inches? • 350 • 240 • 470 • 210 15 Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches): ŷ = -210 + 5.6x. Shawna's dad’s height is 72 inches and he weighs 182 pounds. What is the residual of weight and height for Shawna's dad? • 11.2 pounds • 193.2 pounds • -11.2 pounds • 809.2 pounds 16 For the plot below the value of r2 is 0.7783. Which of the following sets of statements is true? • About 78% of the variation in distance flown can be explained by the ticket price. The correlation coefficient, r, is 0.606. • About 78% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882. • About 88% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882. • About 22% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.606. 17 The scores of the quizzes of five students in both English and Science are: English Science Student 1 6 8 Student 2 5 5 Student 3 9 6 Student 4 4 7 Student 5 8 9 For English, the mean is 6.4 and the standard deviation is 2.0. For Science, the mean is 7 and the standard deviation is 1.6. Using the formula below or Excel, find the correlation coefficient, r, for this set of scores. Answer choices are rounded to the nearest hundredth. • 0.50 • 0.42 • 0.05 • 0.23 18 This scatterplot shows the performance of an electric motor using the variables speed of rotation and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot. • Form: The data points are arranged in a curved line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are far apart from each other. • Form: The data points are arranged in a curved line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are far apart from each other. • Form: The data points appear to be in a straight line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are closely concentrated. • Form: The data points appear to be in a straight line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are closely concentrated. [Show More]

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