3. For the density curve displayed below, what is the mean?

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Clifford Wood
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1 Name: Date: 1. Which of the following statements about a density curve are FALSE? A) A density curve always has area beneath it equal to 1. B) A density curve can adequately describe outliers observed in data. C) A density curve is always on or above the horizontal axis. D) A density curve comes in many shapes, some of which are symmetric while others are skewed. E) The area under a density curve above any range of values is the proportion of all observations that fall in that range. 2. Which of the following statements about the mean and the median of a density curve are FALSE? A) The median is the point on the axis that divides the area under the density curve in two equal halves. B) The median and the mean have the same value if the density curve is symmetric. C) The mean is the balance point of the density curve. D) The median of a skewed density curve is pulled away from the mean in the direction of the long tail. E) For a symmetric density curve, both the mean and the median are at the center of the curve. 3. For the density curve displayed below, what is the mean? A) 0.25 B) 0.50 C) 0.71 D) 0.75 Page 1

2 4. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student owns. B) Number of credit hours taken during that semester. C) The time the student waited in line at the bookstore to pay for his/her textbooks. D) Home state of the student. Use the following to answer question 5: Many residents of suburban neighborhoods own more than one car but consider one of their cars to be the main family vehicle. The age of these family vehicles can be modeled by a Normal distribution with a mean of 2 years and a standard deviation of 6 months. 5. What percentage of family vehicles is between 1 and 3 years old? A) Cannot be determined based on the information given. B) 68% C) 95% D) 99.7% 6. The time to complete an exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the rule, what percentage of students will complete the exam in under an hour? A) 68% B) 32% C) 16% D) 5% Use the following to answer question 7: The number of Facebook friends students at a university have are Normally distributed with a mean of 1,200 and a standard deviation of What percent of students have at least 1000 Facebook friends? A) 84.13% B) 15.86% C) 42.07% D) None of the above. Page 2

3 8. The variable Z has a standard Normal distribution. Find the value z such that 85% of the observations fall below z. A) z = 1.04 B) z = 0.80 C) z = 0.85 D) z = When examining a scatterplot for strength, you are looking to see. A) how close the points in the scatterplot follow a line B) how close the points in the scatterplot follow a curve C) All of the above. D) None of the above. 10. An outlier is. A) a point in a scatterplot that follows the same pattern as the other points B) a point in a scatterplot that does not follow the same pattern as the other points C) All of the above. D) None of the above. 11. If you have two quantitative variables, one way to study them is to use a. A) Scatterplot B) Two way table C) None of the above. 12. When the explanatory variable is categorical and the response variable is quantitative, what type of plot would be appropriate? A) Boxplot B) Time plot C) Scatterplot Page 3

4 Use the following to answer questions 13-15: Malaria is a leading cause of infectious disease and death worldwide. It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The scatterplot shows total precipitation (in mm) in select cities in West Africa on the x- axis and the percent of people tested positive for malaria in the select cities on the y-axis in Precipitation is the variable. A) independent B) dependent C) response D) explanatory E) A and B F) A and D Page 4

5 14. Percent tested positive for malaria is the variable. A) independent B) dependent C) response D) explanatory E) B and C F) A and B 15. The correlation between precipitation and percent tested positive for malaria is probably close to. A) 1 B) 0 C) Can't tell 16. Which one of the following statements is true? A) The correlation, r, measures the strength of the linear relationship between two quantitative variables. B) The correlation, r, measures the strength of the linear relationship between two categorical variables. C) The correlation, r, measures the strength between one quantitative variable and one categorical variable. 17. Positive linear relationships are represented by values of the correlation, r, that are. A) greater than zero B) less than zero C) zero 18. Negative linear relationships are represented by values of the correlation, r, that are. A) greater than zero B) less than zero C) zero 19. The lack of a linear relationship between two quantitative variables is represented by the correlation, r, with values A) greater than zero. B) less than zero. C) equal to zero. D) equal to 1 or -1. Page 5

6 20. As Swiss cheese matures, a variety of chemical processes take place. The taste of matured cheese is related to the concentration of several chemicals in the final product. In a study of cheese in a certain region of Switzerland, samples of cheese were analyzed for lactic acid concentration and were subjected to taste tests. The numerical taste scores were obtained by combining the scores from several tasters. A scatterplot of the observed data is shown below: Taste Rating Lactic Acid What is a plausible value for the correlation between lactic acid concentration and taste rating? A) B) 0.7 C) 0.07 D) In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. price = horsepower Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? A) $41,677 B) $35,000 C) $28,323 D) $13,354 Page 6

7 22. Which of the following statements about least-squares regression involving two quantitative variables, x and y, is (are) TRUE? A) A change of one standard deviation in x corresponds to a change of r standard deviations in y. B) The least-squares regression line always passes through the point ( x, y ). 2 C) The square of the correlation, r, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x. D) The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible. E) All of the above are true. 23. A(n) is an observation that is substantially different from the other observations. A) outlier B) lurking variable C) confounding variable D) None of the above. 24. If you have two categorical variables, one way to study them is to use a. A) Scatterplot B) Regression line C) Two way table Use the following to answer questions 25-26: Suppose you want to determine if there are differences in the average prices among items at three local supermarket chains. 25. What type of study would work best? A) An observational study B) An experiment 26. To reduce bias, how should you select the items to use in your study? A) Choose items which you know are commonly purchased. B) Randomly select an appropriate number of times from a list of all possible items in the supermarket. C) Choose only brand named items. Page 7

8 Use the following to answer questions 27-28: A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions. 27. Fill in the blank. The number 70.24% is a. A) statistic B) parameter C) sample D) population 28. What type of sampling method was used to collect the data? A) A simple random sample. B) A stratified random sample. C) A probability sample in which each person in the population has the same chance of being in the sample. D) Voluntary response. Use the following to answer question 29: Olivia is planning to take a foreign language class. To research how satisfied other students are with their foreign language classes, she decides to take a sample of 20 such students. The university offers classes in four languages: Spanish, German, French, and Japanese. She will select a simple random sample of five students from each language. 29. What sampling technique is Olivia using? A) A simple random sample. B) A stratified sample. C) A multistage sample. D) None of the above. Page 8

9 30. A sample is to be selected from a large population using simple random sampling. The proportion of subjects in the sample that have a given characteristic is to be calculated. Which of the following best describes the sample proportion? A) It is a parameter. B) It is a statistic, which is unbiased for the population parameter only if the population is at least 100 times larger than the sample. C) It is a statistic that is unbiased and its variability does not depend on the population size provided the population is at least 100 times larger than the sample. D) It is a lurking variable whose value is unknown. E) It is a statistic, but its behavior cannot be determined because only one sample is to be taken. Page 9

10 Answer Key 1. B 2. D 3. B 4. A) categorical, B) quantitative, C) quantitative, D) categorical 5. C 6. C 7. A 8. D 9. C 10. B 11. A 12. A 13. F 14. E 15. B 16. A 17. A 18. B 19. C 20. B 21. C 22. E 23. A 24. C 25. A 26. B 27. A 28. D 29. B 30. C Page 10

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student