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An exam is given to students in an introductory statistics course. Comment on the expected shape of the histogram of scores if: a. the exam is very easy b. the exam is very difficult c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes higher-level math skills Explain your reasoning in each case.

Wikipedia gives the following data on percentage increase in population between 2010 and 2015 for the 50 U.S. states and the District of Columbia (DC) (en.wikipedia.org /wiki/List_of_U.S._states_by_population_growth_rate, retrieved October 16,2016 ). Each state is also classified as belonging to the eastern or western part of the United States: a. Construct a stem-and-leaf display for the entire data set. b. Comment on any interesting features of the display. Do any of the observations appear to be outliers? c. Now construct a comparative stem-and-leaf display for the Eastern and Western states. Write a few sentences comparing the two distributions.

Using the five class intervals 100 to \(<120,120\) to \(<140, \ldots, 180\) to \(<200,\) construct a frequency distribution based on 70 observations whose histogram could be described as follows: a. symmetric b. bimodal c. positively skewed d. negatively skewed

The accompanying data on annual maximum wind speed (in meters per second) in Hong Kong for each year in a 45 -year period are from an article that appeared in the journal Renewable Energy (March 2007). Use the data to construct a histogram. Is the histogram approximately symmetric, positively skewed, or negatively skewed? Would you describe the histogram as unimodal, bimodal, or multimodal? \(\begin{array}{lllllllll}30.3 & 39.0 & 33.9 & 38.6 & 44.6 & 31.4 & 26.7 & 51.9 & 31.9 \\ 27.2 & 52.9 & 45.8 & 63.3 & 36.0 & 64.0 & 31.4 & 42.2 & 41.1 \\ 37.0 & 34.4 & 35.5 & 62.2 & 30.3 & 40.0 & 36.0 & 39.4 & 34.4 \\ 28.3 & 39.1 & 55.0 & 35.0 & 28.8 & 25.7 & 62.7 & 32.4 & 31.9 \\ 37.5 & 31.5 & 32.0 & 35.5 & 37.5 & 41.0 & 37.5 & 48.6 & 28.1\end{array}\)

Gave the following data on saturated fat (in grams), sodium (in \(\mathrm{mg}\) ), and calories for 36 fast-food items. a. Construct a scatterplot using \(y=\) calories and \(x=\) fat. Does it look like there is a relationship between fat and calories? Is the relationship what you expected? Explain. b. Construct a scatterplot using \(y=\) calories and \(x=\) sodium. Write a few sentences commenting on the difference between this scatterplot and the scatterplot from Part (a). c. Construct a scatterplot using \(y=\) sodium and \(x=\) fat. Does there appear to be a relationship between fat and sodium? d. Add a vertical line at \(x=3\) and a horizontal line at \(y=\) 900 to the scatterplot in Part (c). This divides the scatterplot into four regions, with some points falling into each region. Which of the four regions corresponds to healthier fast-food choices? Explain.

In a survey of 100 people who had recently purchased motorcycles, data on the following variables were recorded: Gender of purchaser Brand of motorcycle purchased Number of previous motorcycles owned by purchaser Telephone area code of purchaser Weight of motorcycle as equipped at purchase a. Which of these variables are categorical? b. Which of these variables are discrete numerical? c. Which type of graphical display would be an appropriate choice for summarizing the gender data, a bar chart or a dotplot? d. Which type of graphical display would be an appropriate choice for summarizing the weight data, a bar chart or a dotplot? \(?\)

For each of the five data sets described, answer the following three questions and then use Figure 2.2 to choose an appropriate graphical display for summarizing the data. Question 1: How many variables are in the data set? Question 2 : Is the data set categorical or numerical? Question 3: Would the purpose of the graphical display be to summarize the data distribution, to compare groups, or to investigate the relationship between two numerical variables? Data Set 1: To learn about credit card debt of students at a college, the financial aid office asks each student in a random sample of 75 students about his or her amount of credit card debt. Data Set 2: To learn about how number of hours worked per week and number of hours spent watching television in a typical week are related, each person in a sample of size 40 was asked to keep a log of hours worked and hours spent watching television for one week. At the end of the week, each person reported the total number of hours spent on each activity. Data Set 3: To see if satisfaction level differs for airline passengers based on where they sit on the airplane, all passengers on a particular flight were surveyed at the end of the flight. Passengers were grouped based on whether they sat in an aisle seat, a middle seat, or a window seat. Each passenger was asked to indicate his or her satisfaction with the flight by selecting one of the following choices: very satisfied, satisfied, dissatisfied, and very dissatisfied. Data Set 4: To learn about where students purchase textbooks, each student in a random sample of 200 students at a particular college was asked to select one of the following responses: campus bookstore, off-campus bookstore, purchased all books online, or used a combination of online and bookstore purchases. Data Set 5: To compare the amount of money men and women spent on their most recent haircut, each person in a sample of 20 women and each person in a sample of 20 men was asked how much was spent on his or her most recent haircut.