TEST 9 REVIEW 1. The number of students in a school chorus has increased since the school first opened 6 years ago. The linear regression equation describing the change is, where x represents the year and y represents the number of students. a. Complete the table to determine the residuals for the number of students. Year Number of Students Predicted Number of Students Residual Value 0 22 1 26 2 40 3 59 4 78 5 83 b. Construct a residual plot of the data. c. Do you think a linear model is a good fit for the data? Explain your reasoning. 2. The manager of a small restaurant wants to offer soup and sandwich combination meals for lunch specials. To decide what to include in each special, she records the types of soup and sandwiches customers order for several days. The table shows the results.
a. Create a frequency marginal distribution of the data. b. Construct a relative frequency distribution and relative frequency marginal distribution c. Construct a relative frequency conditional distribution for the four types of sandwiches. d. What can you conclude from the relative frequency conditional distribution? e. Analyze each of the tables and the graph you created to represent the lunch items data. Which do you feel would be most helpful to the restaurant manager when choosing soup and sandwich combinations for lunch specials? Based on the tables and graph, what do you think the specials should be? Explain your choices.
3. A school club sold twenty-one different types of gift wrap as a fundraiser. The table shows how many rolls of each type of gift wrap rolls they sold. Number of Rolls Sold Type of Gift Wrap Number of Rolls Sold Type of Gift Wrap 10 9 14 5 12 10 16 18 6 12 A B C D E F G H I J 8 21 12 10 6 18 10 9 10 14 9 K L M N O P Q R S T U a. Construct a dot plot to represent the data. Use the number line provided. b. Describe the distribution of the data set. c. Determine the five number summary for the data. d. Use the number line to construct a box-and-whisker plot of gift wrap sold. e. Analyze the five number summary and box-and-whisker plot. What conclusions can you draw bout the number of rolls of gift wrap sold? Interpret the data in terms of percents. f. Is the median or the mean a better measure of center of the data set? Explain your reasoning. This box-and-whisker plot represents the number of students in classrooms at a school. a. Is the median or the mean a better measure of center of the data set? Explain your reasoning. b. How many students are represented on the box-and-whisker plot? c. What percent of classrooms have 23 or more students? Explain your reasoning. d. What percent of classrooms have between 17 to 23 students? Explain your reasoning.
4. This histogram represents the high temperatures recorded each day for one month. a. How many days are represented on the histogram? b. How many days had a daily high temperature higher than 86 degrees Celsius? c. Suppose the two measures of center are 82.5 degrees and 83.6 degrees. Which of the values is the mean and which is the median? Explain your reasoning. 5. The table shows the population decline of a small town over a seven-year period. Year 2005 2006 2007 2008 2009 2010 2011 Population (Thousands) 9.4 8.3 8.9 8.0 6.9 6.3 6.6 a. Determine the linear regression equation. b. Predict the population of the town in 2014 if the decrease in its population continues at the same rate. c. Predict the population of the town in 2020 if the decrease in its population continues at the same rat d. Is the linear regression equation a good indicator of what the population will be in future years? Explain your reasoning.
6. The graph shows the relation between time and water level during one cycle of a washing machine. a. Is this relation a function? If so, explain why and identify the type of function. If not, explain why not. b. State the domain and range of this problem situation. c. About how many gallons of water are in the washing machine after 9 minutes? d. Write a short paragraph describing the washing machine s full cycle. 7. The table gives the years since a new car was purchased and the corresponding values of the car. Years Since Value of Car Purchase (dollars) 1 16,900 2 13,500 3 8600 4 7900 5 5400 6 4900 7 3600 8 3000 a. Create a scatter plot of the data on the grid shown. b. Sketch a function that best models the data. c. Determine the linear regression equation and the exponential regression equation for the data. Identify which better models the data. Explain your reasoning. d. Use the regression equation to predict the value of the car 10 years after the car was purchased. How does this value compare to the value you determined in part (d)?
8. Analyze the data sets below. a. Describe the distribution of each data set. b. Predict which of the data sets has a higher standard deviation. Explain your reasoning.