Milestone Unit 4 Statistics Sophia

Exam (elaborations) Milestone Unit 4 Statistics Sophia 1 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 0.23 0.05 0.42 RATIONALE In order to get the correlation, we can use the formula: Correlation can be quickly calculated by using Excel. Enter the values and use the function "=CORREL(". Milestone Unit 4 Statistics Sophia CONCEPT Correlation 2 This scatterplot shows the number of hours a student slept every night and his or her grade point average. The equation for the least-squares regression line to this data is: ŷ = 0.375x + 1.33. What is the predicted GPA for a student who sleeps 2.5 hours per day? Answer choices are rounded to the hundredths place. 2.64 2.46 2.08 2.27 RATIONALE In order to get the predicted GPA when the hours of sleep is equal to 2.5, we simply substitute the value 2.5 in our equation for x. So we can note that: CONCEPT Predictions from Best-Fit Lines 3 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 $0.40, 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. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm. 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 (thickness) increases by 1 cm, the outcome (price) will increase by $0.20 on average. CONCEPT Interpreting Intercept and Slope 4 Which of the following scatterplots shows an outlier in both the x- and y-direction? RATIONALE To have an outlier in the x-direction and y-direction the outlier must be outside of the range of y data and outside the range of x-data. This outlier is below in the y-direction and to the left in the x-direction. CONCEPT Outliers and Influential Points 5 A correlation coefficient between average temperature and ice cream sales is most likely to be __________. between 1 and 2 between 0 and –1 between –1 and –2 between 0 and 1 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 6 Which statement accurately describes the data's form, direction, and strength from the scatterplot below? Form: Linear Direction: Positive Strength: Weak Form: Linear Direction: Negative Strength: Weak Form: Linear Direction: Positive Strength: Moderate Form: Linear Direction: Negative Strength: Moderate 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, even though the direction is clear, the data points are less clustered in a line or curve, so the strength is moderate. CONCEPT Describing Scatterplots 7 A basketball player recorded the number of baskets he could make depending on how far away