a. Yes, it is consistent. a. Positive c. Near Zero

Transcription

1 Chapter 4 Test B Multiple Choice Section 4.1 (Visualizing Variability with a Scatterplot) 1. [Objective: Analyze a scatter plot and recognize trends] Doctors believe that smoking cigarettes lowers lung capacity. To test this they measured the lung capacity (in liters) and the number of cigarettes smoked in a typical day for a sample of adults. Is the scatterplot below consistent with the researcher s hypothesis? a. Yes, it is consistent. Lung Capacity b. No, it contradicts this hypothesis. c. There is no evidence in support or contradiction of the hypothesis. Number of cigarettes smoked per day 2. [Objective: Analyze a scatterplot and recognize trends] The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero? a. Positive b. Negative I Q c. Near Zero Hat Size 3. [Objective: Analyze a scatter plot and recognize trends] The scatterplot below shows the number of tackles received and the number of concussions received for a team of football players for the most recent season. Choose the statement that best describes the trend? Number of concussions Number of Tackles a. Teams that receive a greater number of tackles tend to have a higher number of concussions. b. Teams that receive a greater number of tackles tend to receive a lower number of concussions. c. There is no association between the number of tackles a team receives and the number of concussions. 4. [Objective: Describe an association between two variables] Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot from question (2). a. As hat size increases, IQ scores tend to increase. b. As hat size increases, IQ scores tend to decrease. c. The scatterplot does not show a trend that would indicate an association between hat size and IQ scores. d. Hat size causes IQ to increase.

2 4-2 Chapter 4 Test B Section 4.2 (Measuring Strength of Association with Correlation) 5. [Objective: Interpret the correlation coefficient] Which of the following statements regarding the correlation coefficient is not true? a. A correlation coefficient value of 0.00 indicates that two variables have no linear correlation at all. b. The correlation coefficient measures the strength of the linear relationship between two numerical variables. c. The correlation coefficient has values that range from -1.0 to 1.0 inclusive. d. All of the above are true statements. 6. [Objective: Interpret the correlation coefficient] The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars. The relationship between car length and car weight can be described as a. A strong positive linear relationship b. A moderate positive linear relationship c. A strong negative linear relationship d. A weak negative relationship 7. [Objective: Calculate the correlation coefficient] The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below. a b c d Minutes Calories Calories Minutes

3 Chapter 4 Test B 4-3 For questions (8)-(10), match each scatterplot to one of the correlation coefficients. a. b. c. 8. [Objective: visualizing the correlation coefficient] r = [Objective: visualizing the correlation coefficient] r = [Objective: visualizing the correlation coefficient] r = Section 4.3 (Modeling Linear Trends) 11. [Objective: Understand the components of a linear regression model] Suppose it has been established that home value and Years of college are linearly related, and that the relationship can be modeled using the following equation: Home value = $75,000+$12,500(Years of College). In this model, years of college is the? variable, and home value is the? variable. The two variables have a? linear relationship. a. Dependent; Independent; Positive b. Dependent; Independent; Negative c. Independent; Dependent; Positive d. Independent; Dependent; Negative 12. [Objective: Understand the components of a linear regression model] A concert ticket agent is going to investigate whether an increase in money spent on radio advertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, the response variable is and the explanatory variable is. a. Amount of radio advertisement money spent; concert ticket sales b. Concert ticket sales; amount of radio advertisement money spent c. Slope; intercept d. None of the above Use the following information to answer questions (13)-(15). The following linear regression model can be used to predict ticket sales at a popular water park. ( ) Ticket sales per hour = current temperature F 13. [Objective: Interpret a linear model] What is the predicted number of tickets sold per hour if the temperature is 79 F? Round to the nearest whole ticket. a. About 258 tickets b. About 257 tickets c. About 250 tickets d. About 310 tickets

4 4-4 Chapter 4 Test B 14. [Objective: Interpret a linear model] In this context, does the intercept have a reasonable interpretation? a. Yes, it is reasonable for people to go to a water park when it is 0 F, so park managers might want to know how many tickets they would sell on average on a 0 F day. b. No, at a temperature of 0 F, ticket sales would be and it is not reasonable (or possible) to have negative ticket sales. c. Not enough information available 15. [Objective: Interpret a linear model] Choose the statement that best states the meaning of the slope in this context. a. The slope tells us that high temperatures are causing more people to buy tickets to the water park. b. The slope tells us that if ticket sales are decreasing there must have been a drop in temperature. c. The slope tells us that a one degree increase in temperature is associated with an average increase in ticket sales of tickets. d. None of the above 16. [Objective: Use technology to find a regression equation] The data in the table represent the amount of pressure (psi) exerted by a stamping machine (x), and the amount of scrap brass shavings (in pounds) that are collected from the machine each hour (y). Also shown below are the outputs from two different statistical technologies (TI-83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap brass shavings using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest thousandth. x y a. scrap = ( pressure );slope = 2.019and the intercept is b. scrap = ( pressure );slope = 2.019and the intercept is c. scrap = ( pressure );slope = 2.134and the intercept is d. scrap = ( pressure );slope = 2.134and the intercept is

5 Chapter 4 Test B [Objective: Understand the components of a linear regression model] A horticulturist conducted an experiment on 140 thirty-six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of habanera peppers harvested from the plants. The average amount of plant food given was 17.8 milliliters with a standard deviation of 0.7 milliliters. The average number of habanera peppers harvested was 6.5 with a standard deviation of 1.5. The correlation coefficient was Use the information to calculate the slope of the linear model that predicts the number of habanera peppers harvested from the amount of plant food given. Show your work and round to the nearest hundredth. a b c d. The slope cannot be determined without the actual data. Section 4.4 (Evaluating the Linear Model) 18. [Objective: Critically evaluate a regression model] The following model was created to show the association between the number of massages received per month and self-predicted stress level: Stress level = ( number of massages per month) The coefficient of determination for the model is or 6.6%. Choose the true statement regarding this model. a. The model shows that there is a negative association between stress level and number of monthly massages, but the relatively small coefficient of determination suggests that very little of the variation is explained by the model, so the model is probably not very good at predicting stress level. b. The model shows that getting even one massage a month will decrease your stress level. c. The model shows that on average a person getting no massages will always have a stress level of 10. d. All of the above are true statements. 19. [Objective: Calculate and interpret the coefficient of determination] In the NHL, the correlation between Goals scored per game and minutes on the ice for a team of players is found to be Choose the statement that is true about the coefficient of determination. a. When given as a percent, the coefficient of determination is always between 0 and 100%. b. 2 The coefficient of determination, r, is equal to approximately c. The coefficient of determination states that about 66.88% of the variation in goals scored per game is explained by minutes on the ice. d. All of the above are true statements.

6 4-6 Chapter 4 Test B 20. [Objective: Critically evaluate a regression model] In certain urban regions, it can be shown that there is a strong correlation between the number of bars in the region and the crime rate in the region. Choose the best answer. a. This shows that bars cause crime. b. This shows that crimes cause bars. c. Causation from this data is not appropriate because the study is observational.