Math 227 Spring 2006 Test #1
Math 227 Spring 2007 Test #1 (Feb. 28, 07) Name:________________________
1. List below are ages of motorcyclists when they were fatally injured in traffic crashes. Using the data, find the followings: (note: if you are using TI 83 to find these values, you need to write down the formulas that you should have used) [48 points – 4 points each-]
17 18 27 16 18 34 16 25 28 15 23
24 32 20 23 31 37 21 33 25 31 20
(a). Mean
(b). Median
(c). Mode
(d). Standard Deviation
(e). Variance
(f). Find the z-score for 28 (the age of one motorcyclist).
(g). [pic]
(h). [pic]
(i). The 68th percentile rank.
(j). The percentile rank for 27.
(k). Construct a Box-whisker plot for the data, and discuss the skewness of these data.
(l). Construct a frequency distribution Table. Using 15 as the lower class limit of the first class and 5 as the class width.
2. Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. [8 points]
(a). Salaries of college professors. ______________
(b). Current temperature of the classroom at ELAC. ________________
(c). Survey responses of “good, better, best” ________________
(d). The color of cars driven by college students. ______________
3. The given frequency describes the speeds of drivers ticketed by the town of Poughkeepsie police. These drivers were traveling through a 30 mi/h speed zone on Creek Road, which passes the author’s college. Use this frequency distribution table to answer the following: [24 points-4 each-]
|Speed |Frequency |Class Boundary |Class Midpoint |Relative Frequency | | |
|42-45 |15 | | | | | |
|46-49 |10 | | | | | |
|50-53 |7 | | | | | |
|54-57 |4 | | | | | |
|58-61 |2 | | | | | |
(a). Fill-in the class boundary for each class.
(b). Fill-in the class midpoint for each class.
(c). Fill-in the relative frequency for each class.
(d). Find the mean. (if using TI calculator, write down the formula, and the answer)
(e). Find the standard deviation. (if using TI calculator, write down the formula, and the answer)
(f). Construct the corresponding histogram.
4. Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. [12 points]
(a). Motivated by a student who died from binge drinking, the College of Newport conducts a study of student drinking is randomly selecting 10 different classes and interviewing all of the students in each of those classes. ________________
(b). An NBC television news reporter gets s reaction to breaking story by polling people as they pass the front of his studio. _________________
(c). In a Gallup poll of 1059 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers that were called. _____________________
(d). A quality control engineer selects every 100th computer power supply unit that passes on a conveyor belt. ________________________
5. Which is relatively better: A score of 85 on a psychology test or a score of 42 on a math test? Scores on the psychology test have a mean of 90 and a standard deviation of 10. Scores on the math test have a mean of 55 and a standard deviation of 5. Explain your answer. [6 points]
6. Determine whether the given values are from a discrete or continuous data set. [4 points]
(a). A statistics student obtains sample data and find that the mean weight of cars in the sample is 3126 pounds. ________________________
(b). The numbers of eggs that hens lay. __________________
7. The score of a statistics test has mean of 38 and a standard deviation of 3.2. [12 points]
(a). Is a core of 47.0 considered “unusual”? Why or why not?
(b). What can you conclude from Chebyshev’s theorem about the percentage of students score between 30 and 46?
(c). If the scores have a bell-shaped distribution, what is the approximate percentage of women between 31.6 and 44.4?
8. Identify the sample and the population. Also determine whether the sample is likely to be representative of the population, why? [6 points]
“A reporter of Newsweek asks10 randomly selected adults if they feel that the current president is doing a good job.”
Sample: ____________________
Population: ____________________
Representative? ______________________
9. Kelly gets test grades of 65, 83, 80, and 90. She gets a 82 on her final exam, and she gets a 75 on her project. Find the weighted mean if the tests count as 15% each, the final exam count as 30%, and the project count as 10%. [6 points]
10. The following data show the method of payment by 16 customers in a supermarket checkout line. Here, C refers to cash, CK to check, CC to credit card, D to debit card, and O stands for others. [12 points, 6 each]
C CK CK C CC D O C
CK CC D CC C CK CK CC
(a). Construct a frequency distribution table.
(b). Draw a pie chart.
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