Sophia Introduction to Statistics Unit 4 Milestone 4., Exams of Statistics

Download Sophia Introduction to Statistics Unit 4 Milestone 4. and more Exams Statistics in PDF only on Docsity! SOPHIA CHALLENGES, MILESTONES, AND TOUCHSTONES ee *F SOPHIA & UNIT 4 — MILESTONE 4 - HEADMAN Score 15/18 You passed this Milestone 15 questions were answered correctly. 3 questions were answered incorrectly. 1 The table below shows the grade and reading level for 5 students. Grade Reading Level Student 1 2 6 Student 2 6 14 Student 3 5 12 Student 4 4 10 Student 5 1 4 For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth.  1.00 The explanatory variable is what is along the horizontal axis, which is distance. The response variable is along the vertical axis, which is cost. CONCEPT Explanatory and Response Variables 4 Data for weight (in pounds) and age (in months) of babies is entered into a statistics software package and results in a regression equation of ŷ = 17 + 0.8x. What is the correct interpretation of the slope if the weight is the response variable and the age is the explanatory variable?  The weight of a baby increases by 0.8 pounds, on average, when the baby's age increases by 1 month.  The weight of a baby decreases by 17 pounds, on average, when the baby's age increases by 1 month.  The weight of a baby increases by 17 pounds, on average, when the baby's age increases by 1 month.  The weight of a baby decreases by 0.8 pounds, on average, when the baby's age increases by 1 month. RATIONALE When interpreting the linear slope we generally substitute in a value of 1. So we can note that, in general, as x increases by 1 unit the slope tells us how the outcome changes. So for this equation we can note as x (age) increases by 1 month, the outcome (weight) will increase by 0.8 pounds on average. CONCEPT Interpreting Intercept and Slope 5. This scatterplot shows the performance of a thermocouple using the variables temperature difference and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot.  Form: The data pattern is linear. Direction: There is a positive association between temperature difference and voltage. Strength: The data pattern is strong.  Form: The data pattern is nonlinear. Direction: There is a positive association between temperature difference and voltage. Strength: The data pattern is weak.  Form: The data pattern is nonlinear. Direction: There is a negative association between temperature difference and voltage. Strength: The data pattern is weak.  Form: The data pattern is linear. Direction: There is a negative association between temperature difference and voltage. Strength: The data pattern is strong. RATIONALE If we look at the data, it looks as if a straight line captures the relationship, so the form is linear. The slope of the line is positive, so it is increasing. Finally, since the dots are closely huddled around each other in a linear fashion, it looks strong. CONCEPT Describing Scatterplots 6. In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. Which of the following statements is TRUE?  93% of the high school students studied lost weight.  There is a strong positive linear association between weight loss and exercise, but the researchers have not proven causation.  The researchers proved that exercise causes weight loss.  The researchers proved that exercise causes weight loss, but only for high school students. RATIONALE Recall that correlation measures the strength and direction of linear association. So r= 0.93 indicates a strong positive linear association. Recall also, that correlation doesn't imply causation. Causation is a direct change in one variable causing a change in some outcome. CONCEPT Correlation and Causation 7. A correlation coefficient between average temperature and ice cream sales is most likely to be __________.  between 0 and –1  between 0 and 1  between 1 and 2  between –1 and –2 RATIONALE In general as temperature increases, tastes for ice cream goes up. So the correlation should be positive, which would be between 0 and 1. CONCEPT Positive and Negative Correlations 8 RATIONALE To have an outlier in the x-direction the outlier must be in the range of y data but outside the range of x- data. CONCEPT Outliers and Influential Points 12 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?  549.54  383.55  483.55  417.56 RATIONALE In order to get the predicted calories when the grams of fat is equal to 25, we simply substitute the value 25 in our equation for x. So we can note that: CONCEPT Predictions from Best-Fit Lines 13 A basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball net. The distance from the net (in feet) is plotted against the number of baskets made as shown below. Using the best-fit line, approximately how many baskets can the player make if he is standing ten feet from the net?  9 baskets  5 baskets  8 baskets  3 baskets RATIONALE To get a rough estimate of the number of baskets made when standing 10 feet from the net, we go to the value of 10 on the horizontal axis and then see where it falls on the best-fit line. This looks to be about 5 baskets. CONCEPT Best-Fit Line and Regression Line 14 Brad 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 neighborhoods across the country. The plot shows a strong positive correlation. Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his 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 health insurance costs in the United States  The number of citizens in the United States who do not have health insurance  The number of different car brands  Average annual salary per household RATIONALE Recall that a lurking variable is something that must be related to the outcome and explanatory variable that when considered can help explain a relationship between 2 variables. Since higher income is positively related to owning more cars and having health insurance, this variable would help explain why we see this association. CONCEPT Correlation and Causation 15 Shawna finds a study of American women that has an equation to predict weight (in pounds) from height (in inches): ŷ = -260 + 6.6x. Shawna's mom’s height is 68 inches and her weight is 179 pounds. We can also note that r = . CONCEPT Coefficient of Determination/r^2 18 For ten students, a teacher records the following scores of two assessments, Quiz 1 and Test. Quiz 1 (x) Test (y) 15 20 12 15 10 12 14 18 10 10 8 13 6 12 15 10 16 18 13 15 Mean 11.9 14.3 Standard Deviation 3.3 3.5 The correlation of Quiz 1 and Test is 0.568. Given the information below, what is the slope and y-intercept for the least-squares line of the Quiz 1 scores and Test scores? Answer choices are rounded to the hundredths place.  Slope = 0.60 y-intercept = 1.22  Slope = 0.60 y-intercept = 7.16  Slope = 0.54 y-intercept = 1.71  Slope = 0.54 y-intercept = 1.22 RATIONALE We first want to get the slope. We can use the formula: To then get the intercept, we can solve for the y-intercept by using the following formula: We know the slope, , and we can use the mean of x and the mean of y for the variables and to solve for the y-intercept, . CONCEPT Finding the Least-Squares Line